Product Description

Customer Reviews (5)

A Great Book for Getting to know Abstract Algebra
I am in a abstract algebra class and am using this book along side my text.Unlike my text the book explains the ideas behind the mathematics involved and gives relevant examples of what it is talking about.It does not follow my book exactly in order, but it does have a section on all the topics in the book.I would suggest using this book along (or instead of) side of any text on abstract algebra.

Superb introduction to abstract algebra
I fully agree with the comments of the previous reviewers. This introductory book on abstract algebra is simply superb.
The author uses a discursive language, pretty unusual for a book of this type but extremely effective. While going through this book, you have the impression not of reading a textbook but of "listening" to the author talking to you.
I am not a professional mathematician, and therefore I don't feel entitled to judge about its mathematical rigor but I have read and studied similar textbooks on the subject (like Fraleigh and Gallian) and the clarity of this book surpasses them all.
The author provides lots of exercises and some worked out solutions.
Definitively this is my strongest recommendation for a book on this subject.

Superb clarity
The fluent style and abundant examples make it accessible for practically anyone interested. Highly recommended

Hands down the best written book on introductory abstract algebra
This is an excellent book on abstract algebra that makes the transition into this difficult area
as painless as possible. As a engineer who was forced to learn group theory, I looked in at least 50 books
on this subject (another good choice is
Groups and Their Graphs by Grossman)
and Pinter's treatment was the most user friendly treatment I came across.
Also, this book is in no way dumbed-down as it covers similar ground as Fraleigh's well-known text and goes all the way through Galois Theory.

I have no doubt that most physicists and applied scientists would
also love the style of this book. However, ivory tower mathematics types might put their nose up at the
way Pinter develops the material.
Specifically, this book goes to great lengths to show the scaffolding behind the ideas and proofs. Concrete
examples and toy problems are given without apology.
As a result, the
mathematicsis brought alive and not depicted as cold and detached theorem proving. This book actually
is a perfect response to the snobby elitism exuded by many
advanced math texts.Overall, this book is a model of good mathematics texbook writing.My highest recommendation.

One final comment regarding the dover edition of this text -I would also recommend trying to dig up a used hardcover version of the 2nd edition.
The dover edition is typeset in very small print and is hard to read.

Don't let this book be the one that got away...
Each class I've taken as a grad student, I've gone a little overboard buying all sorts of books on the subject matter. I like that each author has a unique style and approach.

In abstract algebra, there are the standards (Dummit, Hungerford, etc). These are the more down-and-dirty texts. They're good. They're thorough. They're rigorous. They do the job quite well if you already have some familiarity with the subject.

Then there are the older, cheaper books, like Deskins. It's alright. Some people nay-say it, but whatever: it's cheap and is one more voice to add to the choir.

Pinter, though, reads like a novel---and not in a cheesy way. As I waited for a friend in Barnes and Noble, I half-heartedly picked it up to skim through it... The introduction hooked me--it sums up what lies ahead like a movie trailer, leaving one mad to find out the whole story. Some might shrug this book off as a lowly"undergraduate" book, but if this is the case, you're missing out on the one author who has been able to deftly convey just how inspiring this subject really is. No other book has convinced me of the power of abstract algebra like this book.

Will it be the only book you read on the subject? If it is, then it was a good choice.

Having experience with the more standard tomes out there, there is the chance that I think this reads like a novel and is "so good" because I am familiar with the material. But, seriously, this is the kind of book that you're lucky to stumble across, whoever you are: a math nerd, physics geek, bio dweeb, or chem freak. This book will, at the least, open your eyes to well-kept secrets of higher mathematics. ... Read more

Product Description

This long-awaited revision provides a concise introduction to topics in abstract algebra, taking full account of the major advances and developments that have occurred over the last half-century in the theoretical and conceptual aspects of the discipline, particularly in the areas of groups and fields.

Key features include:

• A new section on binary linear codes
• New chapter on Automorphisms and Galois Theory
• 450 fully solved problems and 420 supplementary problems for individual practice
• More than 175 illustrative examples

Customer Reviews (8)

not helpful
This book did not help me at all. It covers a tremendous amount of material. So the outlines are very thin. One has to know the material very well to read this book.
I would have liked to see a lot more detail for Groups, Rings, Fields and Modules, with a lot of worked out problems. And none of the Vector space, Lin Algebra, Matrix and Boolean Algebra stuff. In that way it would help undergrad abstract algebra students.The way this book is written, I can't see who the target audience is right now.

Excellent Abstract Algebra Book - Simple explanation yet cover wide scope
I read about 20 books on Abstract Algebra, but I still find this book excellent for Math students who have not been exposed to Abstract Math before. This book serves as a bridge from High-school 'computational' Math to the University Math which is based on abstract proof of Math structures.

I have not seen a similar excellent book on Abstract Algebra which could cover the vast topics in such systematic manner: from Set, Relation, N,Z,Q,R,C,building a solid foundation, before attacking the 'gems' in Group, Ring, Field, Polynomial, Matrices & Linear Algebra.

The selling point of this book is the 450 exercises at end of each chapter. Keeping the core definitions and theorems at each chapter while leaving the proofs later in the exercises, this allows the reader to browse thru' the topics quickly without being burderned by the nitty-gritty details of proof which would slow down the reading.

Granted, Galois Group is not covered in details. However, one has to compromise that the Galois Group is too advanced a topic to deserve another big volume to cover. The example given 'Gal C/R' explains, to my opinion, a clear view of what Galois Group is: Group of automorphism of functions, sub-field (or splitting field), etc. You can grasp what a Galois Group is in 1 single page, rather than reading a 100-page book but still have a faint idea of what 'Gal K/F' is?

My only comment is there are quite a few typo mistakes in Definitions, Theorem reference numbers, which are easily spotted if you understand the topics.

I sincerely hope there will be a 3rd edition of this book soon.

DON'T BUY THIS BOOK
This book is full of wrong concepts, wrong definitions, misleading explanation, wrong proofs, ... A math book like this is a real shame! I have thrown this book to the garbage!
As it is possible that nobody has corrected this book before putting it in the sale?

this book is out of date
I think that most of schaum's series are out of date. In particular, Schaum's "abstract algebra" is not an exception. I bougut this book to prepare my course, Abstract Algebra 1. But this book was full of stuff which is not relevant to the subject.For example, it deals in matix and boolen algebra, which are excluded in most of Alstract Algebra courses in universities. And it doesn't contains stuff about Galois' Theory. Galois' theory can be called the aim to learn Abstract Algebra. I cannot help confessing that to read this book is to waste time. It would confuse you rather than help. You cannoutbuild the outline of Abstract Algebra with this book. I think that it is becase this book was too old-fashioned.

Full of errors
~I usually gave books I bought not bad reviews. But this one, I hate to put it in this way, is full of wrong concept, unclear definition, misleading explanation, incomplete proof, ... A mathmactics book like this is a real shame!

The reason I did not give it one star was I like Schaum book's style: definition, then example, then exercise, then answer at the end (this one doesn't have).

In sum, you can't use this book for any purpose, except as one reviewer pointed out, the errors really~~ make you think about the concept. But before you can do that, you should already know some basic abstract algebra and have a logic mind.~ ... Read more

Product Description
Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. 24 tables and figures. Rep. of 1971 ed.
... Read more

Customer Reviews (11)

It's all been said: Great book!
It's all already been said: this is a great book if you're looking to thoroughly learn the material yourself, rather than be given proofs. It forces you to prove fundamental ideas for the development of the theory, providing definitions and guidance. It's absolutely full of relevant exercises.
I really liked the style of the book. It felt more like a mathematical discussion rather than a lesson. This was partly due to the many exercises immediately following each definition or theorems, rather than being chunked all at the end of the chapter. I didn't feel like I was being talked down to, which I think is deserved for getting through the exercises myself.
However, it was exactly for these reasons that my boyfriend didn't like the book, so be aware that it just might not be your cup of tea. It's worth trying out, though, considering the low price.

a good book
This book itemizes the related theorems and covers most major results. It would be better if some definitions have some more detailed examples.

A Great Supplement
I recommend this book for all who are taking undergraduate Abstract Algebra. The book gives clear explanation of most of the concepts taught in class. Another great thing about this book is that it includes definitions and explanations of terms that are usually not discussed in class. This is a must have for math majors!

DO NOT READ THIS PLEASE!IT COULD SAVE LIVES!
I think I bought this book only because it had that neat Moor Methodesque presentation.And because I like to buy math books.And because it was cheap.

So far so good, though I can't say that it differs particularly from any standard text on algebra.It's not big enough to be Lang.Not terse enough to by Hungerford.And not comprehensive enough to be Dummit and Foote.
It also costs about a fifth of the price of any of those and has a neat do-it-yourself kind of methodology.

Good Book on Algebra
I wanted to study Galois Theory to understand why the quintic is not solvable in radicals.I did some search on the net and ran into this book. My math background is in probability and analysis. With my background and interest this book I feel this book is perfect. It is not too difficult, plenty of exercises and I can follow the development; also I do not feel I am being talked down to by the author.I will have a good understanding of Galois and related theories after putting in the time and effort with this book. ... Read more

Product Description
Contemporary Abstract Algebra 7e, written by Joseph Gallian, a well-known active researcher and award-winning teacher upholds the text's reputation for providing students a solid introduction to traditional abstract algebra topics. The text includes concepts and methodologies used by working mathematicians, computer scientists, physicists and chemists. ... Read more

Customer Reviews (41)

One of about 3 "best texts" on this in 2000
Good for 2nd course. First would be perhaps Saunders MacLane , Algebra, or Herstein, Topics in Algebra.

What is so great about these newer books is more examples worked out and more exercises. I love to work the exercises -- I learn as much from that as from the lectures and regular homework.

Good, but not great
Abstract algebra is an inherently abstract, formal, non-intuitive subject, and while it can be made less difficult, it cannot be made easy. Gallian's book is a valiant attempt at the latter. The book shies away from precise definitions, formal proofs, and that elusive thing known as "mathematical maturity." However, abstract algebra simply cannot be satisfactorily taught without at least a minimum of these things, and is best taught in as formal of an environment as possible. As such, I cannot recommend Gallian's book to those who wish to learn abstract algebra on a late undergraduate/beginning graduate level. However, for the advanced high school student who wishes to study abstract algebra early, Gallian's book is excellent in that it does not presume that the student has had much prior exposure to advanced mathematics.

Excellent for an Easy Start!
This is a great textbook for an introduction to group theory, however, it's not the textbook you want if you want a strong foundation. That's what Dummit and Foote is for.

For the price (used), it was very reasonable, and a nice addition to my collection of math texts.

One of the worst Abstract Algebra Books ever
This book actually develops very little math in its chapters , while throwing some very difficult problems at the reader.It is really surprising that in order to read an essential theorem like Cayley's Theorem (page 126) one is referred back to Exercise 23 , and to Exercise 9.Can't Dr Gallian have at least one self-contained Proof?? I can see that maybe he wants to make the student think , but the book has plenty of exercises for that purpose!Example 14 on page 208 is also very revealing.Here Dr Gallian talks about a very important isomorphism,but he just mentions a lot of facts without proof in the body of his proof!!!Really amazing!What can a student seeing this stuff for the first time learn from this example?? Beyond the bad presentation here are some major defects :
1.Compared to other popular Algebra textbooks used these days in the U.S , the Exercises are very difficult.I made comparisons to 3 other popular textbooks.The Exercises are harder than "A First Course In Abstract Algebra" by Fraleigh.It is harder than "Elements of Modern Algebra" by Gilbert and Gilbert , and finally it is harder than "Abstract Algebra" by Blair and Beachy.
2.It is well known to Undergraduate Educators like myself , that most students who are in undergrad math programs have no intention of going to Graduate School in Mathematics.For most of these folks it was a Shock to learn that the Undergraduate Abstract Algebra Course has a lot to do with proofs , and little with Computations.This book just adds to this Shock.It is certainly not in tune with current academic reality facing Abstract Algebra Instructors,due to the fact that it expects too much from the student.
3.In recent editions the book has become more and more applications oriented.This is completely unneccessary , and I really do not know what Dr Gallian is trying to accomplish here.
4.It seems to me that Dr Gallian has had the same approach one would have when writing a Calculus textbook: But this approach does not work in a hard subject like Abstract Algebra .This Book does not provide any insights into the actual thought processes that are required in constructing airtight Abstract Algebra Proofs. Throughout the book, one is constantly left with the question "So what are the important problems and techniques?"Dr Gallian's approach would have been perfectly OK if he was writing a Calculus book , because in Calculus just looking at a few model problems is enough to master the subject to a reasonable degree.However in higher level math courses due to the huge number of different methods and its variations , it is more important to develop insights into the subject.
This will not happen when studying this textbook.I consider this to be the BIGGEST FLAW of the book.
Conclusion: This is a very bad Abstract Algebra Book.AVOID this book if you are trying to learn something about the subject.

No good.
Like most textbooks on abstract algebra (group theory), this book has no reason for existence.You can't learn from it; the student solutions manual provides only limited "help", the chapters are too discursive, haphazard and in general so abstract as to defy comprehsnion by the ostensible reader (student).In short, the book provides no understanding of the subject, for the author does not know how to start from the beginning and build.

If his book is any indication of the way he teaches, I would hate to be one of Mr. Gallian's students, for despite my best efforts, I would probably end up leaning nothing and find myself unable to put it all together..

It's obvious that Mr. Gallian does not care about his reader.Two circumstances support this:

Mr. Gallian's proof of Cayley's theorem is obviously intended for someone already familiar with it for among other things,it is presented without motivation and without concreteness.This shortcoming is not unique to Mr. Gallian, for I tried at least four other sources before finding one which starts at the beginning.

The discussion of the computation of Aut(Z10) is incomprehensible, again due to Mr. Gallian's disdain for providing even the simplest motivation--in short, he does not nkow how to start at the beginning.Mr. Gallian apparently expects us to intuit that because an isomorphism takes an element from order K to another element of order K, (U(10) is isomorphic to AutZ(10).I know that I don't express this well--but that's for Mr. Gallian to do.Incidentically, Mr. Gallian's treatment of the isomorphism of (Zn) to (U(n)is just as baffling.I, for one, don't expect genuis from a textbook, only clarity.

I should not have to remind Mr. Gallian that abstraction is engendered from the concrete.He has been teaching long enough to know this.

Books like his are one of the reasons why people are turned off to math in general.

P.S.I am still looking for a good (read clear, logical, organized) textbook on abstract algebra (group theory).

... Read more

Customer Reviews (14)

Ok Textbook
Bought this book for a class.It makes a tough subject a little easier.

one of my favorites
Loved this subject and the book, it has clear proofs and plenty of descriptions of concepts, and it works from the very beginning and builds on itself.I would reccomend it.It is an expensive book, but I got it for a much better price here on amazon, I think it was less than half of what they were asking at the UCLA bookstore.I will certainly be buying my textbooks here from now on.

Great book but SLOW shipping
The book is in pristine condition, as promised. And yes, I chose the cheap, standard shipping, but I've found that usually books still arrive relatively fast. This book, however, took over a month to ship and then over a week after being shipped to finally arrive. So, if you're a poor college kid looking to save a few bucks on shipping you might want to re-evaluate how much it's worth to you to have the book arrive in a timely manner.

Undergraduate Abstract Algebra
This is a great introduction to abstract algebra. I really like this book and it goes through examples and proofs enough for you to understand even if you have to go back over them again. I have used this book in my undergraduate studies. I highly recommend it and Hungerford's approach is different from most modern algebra texts because he introduces ring theory before group theory. Even if this book is not your text and I am sure it would be good help as a supplementary one. It even has solutions, answers or hints to some of the odd numbered exercises. This book will really get you to understand modern algebra if you take the time.

PERFECT For Self Study
If you're looking to gain experience in with algebra before you take a honors class or are just interested in self-study have some limited knowledge of the field, then Hungerford is the book for you!It is clear, concise, and there is a plethora of problems that range from computational to challenging.Even if you have a very limited background, the appendix provides a great reference for anyone.

If you're using a book such as Herstein's Topics In Algebra, this provides agreat supplement, since you can practice in the easier problems and then be prepared to tackle Herstein's more difficult problems. ... Read more

Product Description

Considered a classic by many, A First Course in Abstract Algebra, Seventh Edition is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.

Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gröbner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra

For all readers interested in abstract algebra.

Customer Reviews (26)

best first abstract algebra book
I enjoyed reading this book very much. It is very appropriate for first time study of abstract algebra.
Pros: Very well written, easy to read. Examples and answers to odd problems. Each chapter is written for a 50 min class, good for pacing yourself when self studying. Enough material for more than 1.5 semesters. All chapter exercises are broken down in 3 categories: computations, concepts and theory.
Cons: none

Sufficient to master basic elements in algebra
This book provides a pretty nice track on group, ring, vector space and toward Galois theory. It is not a easy book, i.e. people who want to self study may feel frustrated. When I read the proof, sometimes I felt like doing exercise. Abstract algebra is indeed abstract, so example are extraordinary important. The examples in the text is not enough, thus doing problems are absolutely required.

However, I still trying to emphasis my positive opinion on this book: most due to clarity and completeness. Theorems are very organized, not cumbersome. Proof are succinct and suitable for review. This book almost covers all important topics in fundamental algebra, thus become a very good reference.

Worst Math Book I've Ever Used
I have a Master's in Engineering and I'm a A+ student when it comes to math.Yet I've never struggled so much in a class and the book was not help. It provided almost no examples and would say things like "this is obvious."Well, it wasn't to me!Also, it was not clear at all how to solve the problems in the book from reading the section.

If you're a professor, please consider the student's perspective.This subject is challenging and it's no help giving them a book that doesn't have good worked examples.

Terrible book
Terrible book, that was extremely overpriced.It had bad examples and few that pertained the the practice problems.it gave no insight into proofs.

Fraleigh?awesome, sure
This book was my introduction to algebra, and I can say that with me it hit its target - I not only learned and understood abstract algebra, but I grew to love it and be thrilled by it.If you are outside of mathematics and looking for the way in, I don't think you can do much better than Fraleigh.You'll outgrow it - almost as soon as you put it down.But that's just testament to how far it can take you in just a dozen or so chapters.

I would recommend, if you can afford it, also buying a copy of a zippier book like Hungerford or Dummit & Foote (ask around) and using it together with Fraleigh.Fraleigh won't let you down in terms of giving you the space you sometimes need to grasp things (for example, he gives Tons of examples, and there are plenty of easy exercises that allow you to soak in patterns in the structures for yourself) and an advanced book will give you increased perspective and power. ... Read more

Product Description
This text is intended for a one- or two-semester undergraduate course inabstract algebra and covers the traditional theoreticalaspects of groups, rings, and fields. Many applications are included, including coding theory and cryptography. The nature of the exercises ranges overseveral categories; computational, conceptual, and theoretical problems areincluded. ... Read more

Customer Reviews (2)

good book on abstract algebra
This is a good book on abstract algebra but more exceptionally it is licenced under an open-source documentation licence, and is available in electronic form free at [...]. The book presents group theory, with the Sylow theorems, rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

Abstract indeed.
As part of a basic math course, this book was presented. At first glance, it seemed like a tough one. And indeed it is. Especially the "group" part's in this book is very hard-comprehensible, but hey, maybe that's just me.

For preliminary reading I recommend "Linear Algebra - Gateway To Mathematics" by Robert Messer. This clears up a few things before taking on "Abstract Algebra"

Best regards ... Read more

Product Description
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. ... Read more

Customer Reviews (45)

Great textbook... if you already know everything in it
This book is great if you already know the material.I was taking a first class in Abstract Algebra with this as a textbook, though, and it was completely unenlightening.It seems most suited to being a reference, or a text for a more advanced graduate course.
The style of the book is highly no-nonsense.It basically runs as Definition - Proposition - Proof, and the proofs are not exactly enlightening, leaving many intermediate steps to the reader.I'm sure that would be helpful if I already knew the material, but because I don't, I didn't find the book helpful.

Goodbook for a class
It's a good book with a lot of exercises.
Very good for a graduate class.
Being read with Hungerford is a good combination to prepare for the qual.

The Best Abstract Algebra Textbook!
This textbook is amazing. If you're looking for something more applied, this isn't it. But if you're ready to really dig into abstract algebra, this book will give you a strong base.

The Wordiness is overwhelming
Dummit and Foote's Abstract Algebra book, in terms of content, is one of the best. It should be easily read by any decent student at the advanced undergraduate or early graduate level. They give a lovely arsenal of important examples. The exercises are nice as well. I must give this book 3 stars, because of the annoying superfluous style in which they write. The exposition is consistently redundant and bloated; for example, they'll write,
"Let f(x)/in F[x] be an irreducible polynomial having coefficients in F,"
when they should write,
"Let f(x)/in F[x] be irreducible."
The entire exposition is like this. If they could have written this in a "no-nonsense" fashion, the volume of the book could probably have been cut by at least 40%, and it would be a much more elegant read. The knowledge and understanding potentially gained from this book are like diamonds... buried in a gigantic pile of elephant dung. Speaking for myself, I enjoy math books which are more concise; a good math book should allow a reader to absorb deep concepts and ideas without having to sift through a garbage-mass of words. For example, look at Rudin's Principles of Mathematical Analysis; it is considered to be one of the most elegantly written math books of all time; moreover, the style of baby Rudin is a stark contrast to that of Dummit and Foote.
I recommend the book, by I. Martin Isaacs, "Algebra: A Graduate Course."

A Really Good Textbook but No Solutions!
This is a really good book that explained abstract algebra in a very clear, concise manner.If only it had solutions or hints to its exercises, which it doesn't have any at all,this book would be perfect for an undergraduate introduction to the subject.

The key to learning and understanding abstract algebra is to see lots and lots of worked out examples. ... Read more

Product Description
Highly regarded by instructors in past editions for its sequencing of topics as well as its concrete approach, slightly slower beginning pace, and extensive set of exercises, the latest edition of Abstract Algebra extends the thrust of the widely used earlier editions as it introduces modern abstract concepts only after a careful study of important examples. Beachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture. Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers. ... Read more

Customer Reviews (7)

Very good
I am midway through my second semester of undergraduate algebra using this textbook, but I have been reading ahead and just finished the final chapter.While it gets a little rocky at some points in the later chapters, overall it is very clear and well written.I don't have a lot to write about this book, but part of the reason for that is that when reading textbooks, the bad stands out a lot more than the good does, and so a good textbook leaves you with little to review.The book takes a very number-theoretic approach to algebra, which I personally find somewhat dry, but that's simply a matter of opinion.

Thank you!
Book arrived in excellent condition and very timely manner.Will definitely check out for further textbook purchases.

A very nice, detailed exposition to Abstract Algebra
This is the best introductory text I've read.I like it much better than Durbin, and it's easier to read than Herstein (though Herstein is still a great book!).The author takes a lot of time explaining proofs in the beginning.Over time, they leave more to the reader.The exercises are bountiful, and I often find a few interesting ones in each section.I highly recommend this text to anyone interested in higher mathematics.It's very thorough, yet very readable.

only for brainiacs
This book has some nice proofs in it (though, disappointingly, many key results are "left as an exercise"), and some nice diagrams as well, but it is way too light on methodology. Unless you're blessed with brilliance, inpiration, and limitless free time, avoid this book. I've read many chapters two or three times over and still cannot apply what I've learned to the problems at the end of the chapter. In that respect, this book fails as a student textbook. It is concise enough to serve as a reference, but doesn't offer much for someone who is genuninely interested in the subject but doesn't already know everything.

Buy this book!!
Not only is the best book I have seen on Abstract Algebra, this is the best mathematics book I own. I have used it as a suppliment while studying, in research, and in teaching. It is clear and readable. The authors also have a wonderful web site with scores of resources on the subject. ... Read more

Product Description
Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. With many examples and, at the end of each chapter, a large number of problems of varying levels of difficulty.
... Read more

Customer Reviews (5)

Very good
Most books from Dover Books on mathematics are very good. This one keeps that up. There is nothing to say more than what many have written here. You won't make a mistake with the price to quality factor for this book.

Not perfect but still very nice
I purchased this book to help me prepare for a graduate-level course as an undergrad. The book is written at a good level: not as rigorous as a typical grad textbook, but not as chatty as many modern undergrad textbooks. This allows the reader to focus on the material and have it well-explained without being distracted or treated like a junior high student. The book contains no answers for any of the exercises. If I was not using it for self-study, this wouldn't be a problem. There are a few places where he does a bit of handwaving or is a bit lazy in his definitions (see the definition of "subgroup" on p. 207 for an example), but this does not overly detract from the quality.

While it's not perfect, I'm very happy with the book for my somewhat limited purposes. I'd like to give it 3.5 stars, but I'll be generous and round to 4 since I can't.

A Readable Intro to Algebra
I have worked through the first 7 of the 13 chapters with the exception of chapter 4 (a tangent on Diophantine equations.) My own personal goal was to become acquainted with group and ring theory.If you proceed past chapter 7, then you will learn about polynomial rings, quadratic domains, abstract issues in linear algebra, and other topics.From what I read, I found Deskins' book highly readable.My math background consists of three college courses that I would consider rigorous and proof-oriented.If you have less of a background then it might be more challenging; however, the book builds its concepts very methodically and logically.Rarely did it leave me scratching my head and searching through previous chapters.

Deskins includes enough exercises to get a good mental grasp of the ideas.The level of difficult ranges from the very easy, definition checking problems to the sort of challenging.I say "sort of challenging" because none of the more difficult problems seem to be quite as difficult as the most difficult problems in other books.However, I have no experience with other algebra books, so this may be a characteristic of the subject.

All in all, I highly recommend the book as a text for teaching yourself abstract algebra.It is very readable and the well-chosen exercises help you understand the material.

It's a two-sided thing.
On the one hand, this book, like all Dover Mathematics books, is fairly dense, with few examples or pictures. It's a difficult read, but, again, like all Dover books, is totally comprehensive.

Now, on the other hand,this book is, hands down, the cheapest abstract algebra book you will everfind (again, this is a trait of Dover). When I bought this book on Amazon,I searched for "Abstract Algebra", and despaired when I sawprices like $80.00, $90.00, etc. To find a good textbook for under $20.00is a godsend.

So, basically, if you're willing to put some effort intothis book and plow through it (and it's no more dense, really, than mostmath textbooks), it's very rewarding.

Abstract Algebra provides a clear course in Abstract Algebra
Abstract Algebra provides a helpful look into the great topic of Abstract Algebra.While, like most Dover books, it does not provide extensive amounts of problems or their solutions, Deskins attempts to explain eachtopic from elementary number theory to matrices building upon previousknowledge with the least confusion as possible.Deskins' book does notrequire extensive mathematical background or sheer mathematical genius. Instead, only the desire to learn is required to become enriched by thisbook.I recommend Abstract Algebra to any high-school or colledge studentwishing to expand their mathematical horizons. ... Read more

Product Description

Customer Reviews (7)

exelent book
This book in an excellent choice. Well written not complicated lingo, and for visual learners the diagrams are intelligently selected. Very good introduction to group theory, with many examples. I am a computer programmer so I did not want a book with pure math and this book uses everyday examples to make a point.

Struggling a Little
I am struggling with this book.There are times when more explanation is needed and yet, at other times, there is too much.

Shortest journey from group theory to Galois theory
This book provides the shortest journey from group theory to Galois theory (which determines when a polynomial equation can always be solved by means of an algebraic formula).Any topic in abstract algebra that isn't absolutely essential to this "trip" has been omitted from this book.Hence there's no coverage of ideals of rings, Euclidean domains, etc. The coverage of Galois theory is very rushed and proves only half of the theorem that is the book's ultimate goal; namely, that a polynomial equation can be solved by means of an algebraic formula if and only if the equation's Galois group is solvable.Some of the important proofs later in the book are sketchy.

The reader should be very familiar with methods of proofs and should have had some previous exposure to abstract algebra, especially groups and vector fields.The treatment of Galois theory is so rushed that, for self-study, the reader should refer to a second book on abstract algebra that treats Galois theory -- such as Richard Dean's Elements of Abstract Algebra (1966), which is the basis of the Maxfields' book, or W.E. Deskins' Abstract Algebra (1996).

Excellent text for a first course
I taught out of the hardcover version of this book at SUNY College at Oneonta many moons ago.It was a course for first-semester sophomore mathematics majors.The goal of the book is to develop the subject matter that is needed to prove that the fifth degree polynomial is not solvable by radicals, i.e. there is no analogy to the Quadratic Formula for the quintic.(There is for the cubic and the quartic.)We had a good time because the course was focused on this one goal and the class knew exacly where we were headed.We got there, too.It was very easy to teach from this book and students rated it very highly.The students that I taught had Calculus I and II and a Foundations course as freshmen.The prior exposure to logic, sets and methods of proof (development of the integers) was very helpful, as was the maturity gained from the calculus (although the subject matter of Calculus was not necessary).I supplemented by rigorously developing the rational numbers, saving the reals for the Intro to Analysis course that followed this one.I am now a biostatistician outside of academia, but I hope that professors who are now teaching Abstract (Modern) Algebra will consider using this text in paperback form.

Roots (as in square roots)
This charming little introit to abstract algebra is keyed on a theme of the algebraic equation, and the discovery of the insolubility of the quintic. This includes the history and final plight of the circle-squarers, and some of the history of Galois and Abel, working heroically and heuristically in the early nineteenth century without the recent easier access to the subject now available.
All math is divided into three parts, analysis, algebra, and topology and abstract algebra is no doubt abstract, but less so than analysis, and shows the beautiful hidden sructure behind number systems, from monkey-see monkey-do to counting on your fingers, to the square root of minus one and beyond. The progression from simple groups, to rings, and fields and the rest is a revelation of the complexity behind simple things and it is a pity the educational system cannot bring more to these vistas, where the elegant Galois theory caps the summits. A good book to amateurize with, and with a good mouse-hole entry for a look-see to the ultra-clever Galois theory. Superb. ... Read more

Product Description
Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results. ... Read more

Customer Reviews (16)

Very good
I used this book since it was our textbook in college. It's a great book for starters.

A progressive review
I am going to write this review in progressive style as I am studying it now.

In college, we did use Herstein's other book "Topics in Algebra" but I have found it hard to read. Well... it may well be that I did not work hard enough or did not study it the right way. The reason to pick this book is that he has written a very popular algebra book and this is much thinner than his previous work. It is good to have a simpler and shorter book on any topics before jumping into advanced and sometimes more 'standard' text. It is my dogma that one should find a book best fit for himself/herself.One could always move up the level of difficulty once he masters basic and simpler material.

What I have found in "Abstract Algebra" is pleasant. It could be the case that I am not a total stranger to the field. However, it takes careful planning for an author to decide what should be included in the material, what to be put into the text and what to be placed in exercises.

This book gives some exercises that are the content for future sections. It does so in a good way in that it gives just enough hints without hindering reader's interests (because it's too hard) or spoiling reader's appetite.

Textbooks are supposed to deliver not only the body of knowledge but also to ignite and seduece learners' curiosity as an explorer of the subject matter. It is supposed to transform readers to writers and in this case, researchers. It is supposed to stimulate thoughts and motivate readers to test the water themselves. In mathematics, readers are supposed to be motivated to "discover" theorems beofre it was presented. One of my alumni said that he usually covered up the proof of theorems and try it out himself. It is a good practice. I would think one should do one step futher, to guess and speculate what kind of interesting results one might get by just studying a few examples and definitions. It is suposed to be the fun for math.

My plan is to take it as much time as needed with no rush. Unless I have completed most exercises, left 2-3 at most per section, I will not move forward. If I was postponed moving forward, I will skip sections (as long as it does not hinder my understanding) to learn new material and continuing solving the past unsolved problems. I do constantly recollect the learned sections to have a more personal integrated view of the subject matter so far. (Polya said it's a good practice, and it is indeed.)

It was scheduled to be finished in around 4 months with average pace of 2.5 pages per day. I am late for the progress; not so happy about it. Still have confidnece to finish it before the end of March. I am jumping
ahead to study the Cauchy's theorem and Sylow's theorems before finishing
the "very hard problems" in sections introducing Largrange's theorem.
Hopefully, I could do complete group theory and moving to Ring theory starting Feb. Last evening, figuring out one problem leaving there for three(?) weeks.

Juicy.

Herstein fine, but Amazon didn't send hardcover.
Amazon sent me the softcover while charging me the hardcover price.In trying to exchange, I was told the hardcover was not available, and no refund was given.I needed this book for a class, so it is now annotated and highlighted and I am stuck with an inferior book at full hardcover price.(be careful!)

A Monument to Pedagogical Incompetence
This book clinches for me a caveat to live by in my future mathematical career: Never undertake to learn any new subject in mathematics from a text that is described as "chatty" or "informal". Herstein's prose is mildly amusing up until page 3, whereafter it becomes a nuisance and later a downright irritant. And that's the least of this book's problems.

We start with the first sentence: "For many readers this book will be their first contact with abstract mathematics." That straightaway blows away any excuse Herstein might muster to save face in light of the content on subsequent pages.

First, each section usually has exercises divided into three categories: "Easier", "Middle-level", and "Harder". The easier problems range from mundane pencil-pushing to rather stiff analyses; the mid-level problems are typically quite difficult or nearly impossible; and the harder problems are almost universally intractable - mainly because they have little bearing on what the author discusses. To wit: any problem will be "hard" if you give your student absolutely nothing to go on. To entice a reader to try out a harder problem, the competent instructor knowsto leave a few bread crumbs that lure the reader into the forest. Herstein does not do this. Harder problems are routinely bolts from the blue presented in vacuo, mere non sequiturs in the eyes of the struggling newbie. We need not discuss the so-called "Very Hard Problems" some sections feature, as the mathematical community is still researching them in a feverish competition that surely will bag someone a Fields Medal.

The beginner (the book's alleged target audience) will find section 2.2 utterly demoralizing. The exercises are not categorized as described above, and guess what? They're ALL "harder problems", most of which I still can't solve to this day - and I've moved on successfully to graduate-level abstract algebra. And guess what the title of the section is? "Some Simple Remarks". Herstein is either arrogant beyond the ken of mortal men, or the most sadistic professor to come down the pike since the days of Attila the Hun. By page 50 the book is sending you a clear message: "You are an abject idiot. A gibbering nincompoop. Why are you still even trying?"

Some crucial definitions are couched in the thick of exercise sets where they do not belong. You know, little things like the definition of a cyclic group.

Crucial results used to prove pivotal theorems are sometimes poached from exercises from earlier sections, so the book, damningly, is NOT self-contained. It is inexcusable to have the proof of Cauchy's theorem, for example, hinge on asinine parenthetical statements like "see Problem 31 of Section 4" or "See Problem 16 of Section 3, which you should be able to handle more easily now." What the hell is that about? I've NEVER seen a math text do this at the introductory level. It's gross academic negligence of the highest order. The rule is this: exercises build on definitions and theorems, NOT the other way around!

It's fair to sometimes ask the reader to provide the proof of a lemma, corollary, or minor theorem in an exercise. What is decidedly NOT helpful in the least is scattering the proof of a major theorem all over the map, with some scraps coming before the theorem and remaining scraps coming after. One of Herstein's favorite stunts: a sort of heuristic "hand-waving" argument that weaves around like the Mississippi river, culminating with a statement along the lines of "We have now proved the following theorem...". It's okay to do that once in awhile to break the monotony, but NOT two-thirds of the time in a pathetic attempt to seem less formal and be the student's "buddy". Students of algebra do not need a buddy, they need a teacher who knows how to present material nonrandomly.

The reader almost has to hire a private investigator just to sort out the precise definition of congruence modulo n. What does "a = b mod n" mean? Why, "a ~ b", of course. But what does "a ~ b" mean? Merely that "n | (a - b)", silly goose. Ah, so what does "n | (a - b)" mean?For something so important as the concept of congruence modulo n, one would think its definition would be enshrined right under the bold heading "Definition". But no: it's buried deep in an inane example.

Other times Herstein has it in for private investigators, and right smack in the middle of a theorem readers are reminded that "Ker phi" means "the kernel of phi". Wow, thanks! The only viable explanation for this behavior is that Herstein is violently allergic to theorems that are expressed in only one line; so, he'll pack them with irrelevant crap to ensure they're at least two lines long.

Then there are the tragic expressions of the various correspondence theorems that each utterly fail to mention the relevant correspondence. One concludes with the statement "This sets up a 1-1 correspondence between all the ideals of R' and those ideals of R that contain K." The understandably befuddled novitiate is led to ask: "Well isn't that special. So...what is it?" Herstein seems incapable of placing himself in the shoes of beginners and seeing that what's obvious to him can be a mystery to someone else. An appropriate function must be defined, then demonstrated to be bijective. By no means trivial! Then two pages later 2-by-2 matrices are kicked around like the reader is a drooling imbecile who's never seen them before.

A lot of "examples" are actually fake fronts for exercises, so don't let their apparent abundance bedazzle you overmuch. Others are laughably trivial or ludicrously irrelevant.

Finally, it's breathtaking that Herstein can have an entire section titled "Cycle Decomposition" without ever defining what it means. Just another example of lousy organization and a ham-fisted presentation that never survives the rough-draft version of worthier texts.

More information please!
Most abstract algebra courses are used to give an introduction to the methods of reading/writing of proofs. Herstein seems to have misunderstood the concept of introduction. This is a sink or swim book when it comes to learning how to write proofs! You will surely want to buy an additional book on how to write proofs if your school is using this book for a intro course to abstract algebra. ... Read more

Product Description
If you want top grades and a thorough understanding of abstract algebra this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you sample problems with fully worked solutions, including proofs of all important theorems. You also get additional practice problems to solve on your own, working at your own speed. In addition, this superb study guide gives you chapters on sets, integers, groups, polynomials, and vector spaces. Students' favorite, with more than 30 million copies sold, Schaum's study guides are the best value for your student dollar--clear, complete, and low-cost. ... Read more

Customer Reviews (10)

pleased but only to a point
I really liked this book. It broke down abstract/modern algebra basics very well; however, i thought it would be more detailed about groups (the subject my professor spent much of his time on).It helped with the rules of integers and real numbers and, etc.But I was disappointed with how little of number theory it really covered.I needed to know more about rings and groups and subgroups.If you just need a little help this would be a great book for you.HOWEVER I would suggest looking for a more advanced book if you need information on groups and rings. Good supplementary text, but was not exactly what I thought it was.

I found it invaluable when I was learning modern algebra on my own
Shortly after graduating from college with a math major, I realized that I needed some experience in modern or abstract algebra. For reasons that I no longer recall, I was able to obtain the major without taking a course in algebra. My undergraduate college offered two courses in abstract algebra, but rather than pay the full tuition, I asked the chair of the department if I could take some form of challenge exam for the credit.
She agreed and gave me the complete set of take-home graded questions that she had given out the previous year. I then worked through the exercises and submitted them to her for feedback. I passed both courses.
One of the primary reasons for my achievement was this book. From my perspective, the strongest point of the book is the extensive lead-in before group theory is introduced. The background review in the area of sets, relations, integers, rational, real and complex numbers was something I really needed. These chapters forced me to look at these things in ways that I had not done so in the past and prepared me to better think abstractly.
After this solid introduction, I was able to proceed into the study of groups, rings, integral domains, ideals and fields on my own. By design, the books in the Schaum's series are better used as supplemental rather than core texts. I found this one to be the exception; it is stronger in the preliminaries than it is in presenting the core material of the title.

Average resource
This was an average resource for me in my advanced algebra course.I suggest if you are to use this book, to also get Joseph Gallian's Contemporary Algebra book as well.

lpescatori
Excellent for a quick and rigorous grasping of basic concepts. A huge number of problems helps fix the theory and gain problem solving capability.

Not much on the core subject of abstract algebra
This book has some good theoretical mathematics content, unfortunately not much of it is about the subject of abstract algebra. The first 80 pages of this book talk about sets, relations, operators, and number systems. The next 50 pages or so consist of elementary material ongroups, rings, fields, and polynomials, and act as a very basic introduction to abstract algebra. Then the author again diverges off into mathematics that does not relate to abstract algebra and talks about vector spaces, matrices, matrix polynomials, linear algebra, and boolean algebra. Again, this is all good mathematical material with some good problems, but I don't see what it has to do with learning abstract algebra. A better title for this book would have been "Schaum's Outline on the Foundations of Mathematics" since it is really supplying a good theoretical introduction to mathematics for the mathematics major at about the college sophomore level. If that is what you are looking for, I would give this book about four stars.
If you want a good introductory textbook on abstract algebra might I recommend "A First Course in Abstract Algebra, Seventh Edition" by Fraleigh. The author explains the concepts very clearly, has plenty of examples, and motivates the reader by showing example uses of the theory in applications such as error coding. There are more rigorous books out there, but Fraleigh's book is a great introduction, and used copies can usually be found for roughly $60, or about half of the price of a new book. ... Read more

Product Description
This is a survey, accessible to junior/senior undergraduate students and containing many examples, solved exercises, and sets of problems, of some parts of abstract algebra that are of use in many other areas of discrete mathematics. Three major themes are particularly relevant to computer science, Boolean algebras and switching circuits, finite fields and algebraic coding, and semigroups and automata. The topics of the book can be studied independently of each other, although the book is a mathematics book, the authors have made great efforts to address the needs of the users of the techniques that are being discussed. There is a special emphasis on fully worked out computational examples. More than 500 exercises accompany the 40 sections. This new edition includes major changes to the first edition: corrections and improvements to the first four chapters, a new chapter on Cryptology, and an enlarged chapter on Applications of Groups. An extensive chapter has been added to survey other (mostly recent) applications, many of which were not included in the first edition, nor are commonly found in undergraduate texts. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields. ... Read more

Product Description

This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S. capabilities. Includes “To the Teacher” sections that Draw connections from the number theory or abstract algebra under consideration to secondary mathematics. Provides historical context with “From the Past” sections in each chapter. Features “Worksheets” that outline the framework of a topic in most chapters. A useful reference for mathematics teachers who need to brush up on their abstract algebra skills.

Customer Reviews (2)

Abstract Algebra
The book was shipped promptly.I attended only one class without having the book with me.This was the required book for a class I am taking so I did not really have an alternative.It seems like a very good text.

Today a significant fraction of the students taking this class are students pursuing a license to teach math at the secondary level.It is nice that they have a textbook focused on their needs.

Innovative approach but many errors
I liked the layout and how information was presented. However there were many typos and errors in the book that some times made it difficult to determine if the book or I was in error. Not a good situation. I do think the concept of associating the material to what teachers are teaching in High School is an excellent idea and wish I would see that in all my graduate level math books. If it weren't for many errors due to insufficient proof reading I would have given this book a higher rating. ... Read more

Product Description

This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.

Customer Reviews (8)

nothing abstract in this one
this book is the reason i changed my major from pure to applied mathematics. if you paid attention in your second grade arithmetic class, you won't learn anything new from this book. we used this in my so called "abstract algebra" course, but the author is too narrow minded to think of any algebra outside of arithmetic. i had perfect grades in the class, but i dropped it before the final because i was too disgusted with the presentation. you're better off going with a text on formal language theory like aho and ullman, or maybe algebra by birkhoff and mac lane. you could even write yourself something more informative on a 3 by 5 card.

Just okay.
Not a lot of details in this book.Mostly just theorems and their proofs.

Ugh
This textbook is the first math book I've had that doesn't have any homework answers in the back of the book. Instead, there are "helpful" hints for selected problems that aren't any help at all. This is very frustrating because I never know if I'm getting the right answer or not.

Excellent Introduction To Algebra
Rotman's book is a standard for first courses in Abstract Algebra.The book is easy to read and includes plenty of problems to work on.He even includes several standard syllabi in the preface, depending on the type of course that may be taught with it.It begins with some number theory, then goes into the traditional group and ring concepts.The only reason I would say to not buy this book is if you really don't like the theorem-proof, theorem-proof kind of writing, but if you don't, you're likely not interested in Abstract Algebra anyway.An excellent book for learning as well as reference.

no better than the first edition
It is always easy to add something to than to get rid of something from the book. I guess this is the case of the author when he prepares the second edition. However, I prefer the first edition because it is more readable, enjoyable, and most importantly, contains just enough information for the introduction to abstract algebra. There are huge number of textbooks on abstract algbra, and making another would not be the author's purpose of the revision, I hope, but it looks it is.
By adding more subjects in detail to the second edition, now it looks the same as any other, only to loose its expository and conversational style of writings, and became a reference-style textbook. ... Read more

Product Description

Customer Reviews (3)

good intuitive explanations
I agree with Math Buff, that this book is very helpful due to it's intuitive approach. I am using the online version (which can be found on Ash's website) to complement my lecture on Abstract Algebra.
Whenever I stumble upon something I don't understand, I can usually find a motivation and an intuitive approach in Ash's book.
Though sometimes he does not use the common notation, so you have to keep that in mind!
I printed the book myself since just found this book now - otherwise I'd have bought it!

An average resource
I used this book as a reference resource for an advanced algebra course.At times, wording of key concepts was a little long.This book is a good complementary reference to Joseph Gallian's Contemporary Algebra book.

Intuitive Algebra
This is the book version of a series of lecture notes on abstract algebra written by the author and still available on his web page. However, given the price (it's a Dover book...) it's worth buying just to avoid that thick pile of sheets lying around. The best thing about this book is that it avoids formalism whenever it can without sacrificing rigor. Many theorems are "proved" by means of an example of a general case. In this way, the reader gets the intuition behind the result without having to deal with the abstract and sometimes artificial constructs of a rigorous proof. In any case, supplying that rigorous proof can be seen as an extra exercise (or you can look it up elsewhere!). In other words, it's a great book to learn the ideas behind the theorems dealing with groups, rings, modules and fields.

The second part of the book deals with commutative algebra, algebraic number theory, algebraic geometry and homological algebra - areas where it's very hard to find intuitive explanations in the literature, since books on those subjects tend to assume (quite reasonably) the reader has a solid background in abstract algebra. Unfortunately, that means that examples and intuitive explanations are drastically reduced, sometimes to none at all. That makes this book even more attractive.

In any event, after you get the intuition, it will be much easier to to tackle the more rigorous approaches of Dummit & Foote or Hungerford (I don't know Lang's book but I'm told it's much dryer than these two).
Or you can start your study of algebra with any of these more traditional books and use Ash's as a supplement. If a theorem or its proof proof seems opaque, look it up on Ash. Chances are his explanation will clarify things. ... Read more

Product Description

A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.

Customer Reviews (5)

has great potential, but could use a second edition.
The title of the review pretty much says it all. For a first edition, this isn't bad. I've taken copious notes from this book, and I've learned quite a bit. It's much more comprehensive than most other algebra books on the market, to be sure. I'd be hard pressed to find another introductory algebra book that actually makes it to the Adjoint Functor theorem, tripleability, and Birkhoff's characterization of varieties. However, the book also has its flaws. The most annoying one is probably Lemma 10.6.8 on page 331, which says that afinite dimensional division algebra over an algebraically closed field has dimension 1. This is clearly false. (Consider the quaternions and the complex numbers). The error in the proof is that he assumes commutativity (probably the easiest blunder to make in algebra, so it's a minor offense).Thankfully, no subsequent use of this "lemma" is made in the book (making me wonder why he's choosing to call it a lemma).In some places, Grillet doesn't really have the slickest proof on the market, which would be nice if he's trying to be comprehensive (the book wouldn't be quite as much of a wrist cracker). For instance Jacobson's proof of the simplicity of PSL is much slicker and isolates the hypotheses (dim V >2 or |K|>3) The chapter dependency chart is useful, although he breaks the logic somewhat by using fields in the chapter on group theory.Chapter notes at the end of each chapter would be very useful.
All of these problems can be easily fixed in a second edition. Another idea would be for the author to maintain some sort of errata page (John Lee does this for his books on manifolds). For the most part, the book has great potential because it's got a nice, ambitious logical structure that you won't find elsewhere. I'd rather see someone go out on a limb and try to write a comprehensive, up to date, state of the art algebra book than simply rewrite an existing book focusing only on classical algebra.
For professors who are thinking of using this book for their algebra classes, I'd suggest going through it yourself before the term starts (give yourself a few months) so that you can tweak it a little. That way if you use the book for you class you can catch any mistakes.

Full of Insight
This book does not complicate every concept, on the contrary, and for example, this is the only algebra text I am currently aware of that actually provides insight into the 'mechanics' ofmorphisms between various types of sets.To be precise, in section 1.6 (The Isomorphism Theorems), Grillet, introduces and describes both factoring through a domain and codomain.For the student, this provides insight into what is happening 'behind-the-scenes' in the homomorphism theorem and,in turn, acts as a vehicle that enables the student to fully understand and appreciate the isomorphism theorems.Of course one must take in to account the ability of the student using this text and, given this, I would say Grilet's text requires nothing more than an elementary introduction to the basic algebraic structures.This text is not overwhelmingly wordy like that of Dummit and Foote or baby Hungerford, nor is it stale and lifeless like Lang's.Instead, it is well written, definitely insightful, covers all the material needed at the begining graduate level and this text can be used, like Rotman and Lang's text, as a reference.If this book seems daunting based on the size, then I would recommend either just dealing with it or using Martin Isaacs or Papa Hungerford's since both are complete, challenging and manageable.Enjoy!

Not recommended
A bad textbook I have read for algebra.The author seems to be complicating every concept thats simple to understand.
Also most of the proofs given are not straight forward and forces you to refer to some other books for a clear understanding and definitions of the same concepts given in the book.
Not at all recommended.
Better buy a Fraleigh or Herstein or Thomas Hungerford even if your teacher recommends this one.

Excellent intermediate text
Having used this book in a graduate algebra course, I feel that it is an excellent text for those who have already had a rigorous introductory exposure to modern algebra (say, via Dummit and Foote or Fraleigh).Grillet writes clearly and concisely and leaves several challenging (but doable) proofs to the reader.His wry sense of humor is also reflected in his writing.

On some subjects, it is more of a survey of topics (such as category theory, universal algebras, exterior products), the point of which only becomes clear after one needs to use these tools in other areas.

If you are new to the subject, however, the texts by Dummit and Foote or Fraleigh, e.g., are more appropriate.

another good algebra text
This text is designed for beginning graduate students. The book includes all the basic parts of algebra any mathematician should know. The presentation and proofs are clear and easy to follow. People with no priorexposure to abstract algebra might have problems learning algebra from thisbook as quite a few important theorems and results are left with no proof.Instructor can easily supplement those missing proofs if he/she thinksthat's appropriate. Overall, it's an excellent reference book forresearchers, but only a good textbook for students. ... Read more