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1. Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud | |
Paperback: 797
Pages
(1995-03-30)
list price: US$49.95 -- used & new: US$39.97 (price subject to change: see help) Asin: 0387942696 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
Excellent Book...very atypical for a math book, but I like it!
Not for the beginner
Good book of reference
very good, but should be read slowly
Superb (1) The history of commutative algebra and its connection with algebraic geometry, for example the origin of the concept of an "ideal" of a ring as generalizing unique factorization. (2) The discussion of the concept of localization, especially its origins in geometry. A zero dimensional ring (collection of "points") is a ring whose primes are all maximal, as expected. (3) The theory of prime decomposition as a generalization of unique prime factorization. Primary decomposition is given a nice geometric interpretation in the book. (4) Five different proofs of the Nullstellensatz discussed, giving the reader good insight on this important result. (5) The geometric interpretation of an associated graded ring corresponding to the exceptional set in the blowup algebra. (6) The notion of flatness of a module as a continuity of fibers and a test for this using the Tor functor. (7) The characterization of Hensel's lemma as a version of Newton's method for solving equations. The geometric interpretation of the completion as representing the properties of a variety in neighborhoods smaller than Zariski open neighborhoods. (8) The characterization of dimension using the Hilbert polynomial. (9) The fiber dimension and the proof of its upper semicontinuity. (10) The discussion of Grobner bases and flat families. Nice examples are given of a flat family connecting a finite set of ideals to their initial ideals. (11) Computer algebra projects for the reader using the software packages CoCoA and Macaulay. (12) The theory of differentials in algebraic geometry as a generalization of what is done in differential geometry. (13) The discussion of how to construct complexes using tensor products and mapping cones in order to study the Koszul complex. (14) The connection of the Koszul complex to the cotangent bundle of projective space. (15) The geometric interpretation of the Cohen-Macauley property as a map to a regular variety. ... Read more |
2. Undergraduate Commutative Algebra (London Mathematical Society Student Texts) by Miles Reid | |
Paperback: 168
Pages
(1996-04-26)
list price: US$36.99 -- used & new: US$27.99 (price subject to change: see help) Asin: 0521458897 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
"Undergraduate" in the best way |
3. Introduction To Commutative Algebra (Volume 0) by Michael Atiyah | |
Paperback: 138
Pages
(1994-02-21)
list price: US$71.00 -- used & new: US$64.84 (price subject to change: see help) Asin: 0201407515 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
$1.09 per page.
Favorite book as a grad student
Introduction to Commutative Algebra
Concise Introduction to Commutative Algebra, strong preparation for Algebraic Number Theory and basic Algebraic Geometry
A baptism of fire for Algebraic Geometry For the algebra itself, it also gets on well with Rotman's "Galois Theory" and MacDonald's out-of-print introduction to AG, "Algebraic Geometry - Introduction to Schemes", besides being the perfect preamble in commutative algebra to the books of Mumford and Hartshorne. A gem. ... Read more |
4. Combinatorial Commutative Algebra (Graduate Texts in Mathematics) by Ezra Miller, Bernd Sturmfels | |
Paperback: 420
Pages
(2005-06-21)
list price: US$59.95 -- used & new: US$38.47 (price subject to change: see help) Asin: 0387237070 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers. Customer Reviews (1)
Coherent and Useful |
5. Steps in Commutative Algebra (London Mathematical Society Student Texts) by Rodney Y. Sharp | |
Paperback: 360
Pages
(2001-02-15)
list price: US$50.00 -- used & new: US$42.48 (price subject to change: see help) Asin: 0521646235 Canada | United Kingdom | Germany | France | Japan | |
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6. Computational Commutative Algebra 1 by Martin Kreuzer, Lorenzo Robbiano | |
Paperback: 322
Pages
(2010-11-30)
list price: US$89.95 -- used & new: US$71.97 (price subject to change: see help) Asin: 364208723X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical. |
7. A Singular Introduction to Commutative Algebra by Gert-Martin Greuel, Gerhard Pfister | |
Hardcover: 690
Pages
(2007-12-04)
list price: US$69.95 -- used & new: US$46.52 (price subject to change: see help) Asin: 3540735410 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description From the reviews of the first edition: "It is certainly no exaggeration to say that … A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra … . Among the great strengths and most distinctive features … is a new, completely unified treatment of the global and local theories. … making it one of the most flexible and most efficient systems of its type....another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic....Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike." J.B. Little, MAA, March 2004 The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative rings, a chapter on characteristic and triangular sets with applications to primary decomposition and polynomial solving and an appendix on polynomial factorization including factorization over algebraic field extensions and absolute factorization, in the uni- and multivariate case. |
8. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) by David Cox, John Little, Donal O'Shea | |
Hardcover: 556
Pages
(2006-02-24)
list price: US$59.95 -- used & new: US$45.00 (price subject to change: see help) Asin: 0387946802 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The algorithms to answer questions such as those posed above are an important part of algebraic geometry.This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered it the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century.This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric Theorem proving. In preparing a new edition of "Ideals, Varieties and Algorithms" the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple, Mathematica and REDUCE. Customer Reviews (6)
Symbolic computation
Easiest introduction to Algebraic Geometry
Straightforward and lucidly written
Good book
The best book on the topic |
9. The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics) by David Eisenbud | |
Paperback: 248
Pages
(2005-02-01)
list price: US$44.95 -- used & new: US$27.99 (price subject to change: see help) Asin: 0387222324 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, an appendix provides a summary of commutative algebra, tying together examples and major results from a wide range of topics. Customer Reviews (1)
Great book |
10. A Course in Commutative Algebra (Graduate Texts in Mathematics) by Gregor Kemper | |
Hardcover: 246
Pages
(2010-12-29)
list price: US$59.95 -- used & new: US$51.91 (price subject to change: see help) Asin: 3642035442 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
11. Basic Commutative Algebra by Balwant Singh | |
Paperback: 350
Pages
(2010-12-31)
list price: US$38.00 -- used & new: US$38.00 (price subject to change: see help) Asin: 9814313629 Canada | United Kingdom | Germany | France | Japan | |
12. Combinatorics and Commutative Algebra (Progress in Mathematics) by Richard P. Stanley | |
Paperback: 168
Pages
(2004-10-15)
list price: US$89.95 -- used & new: US$49.98 (price subject to change: see help) Asin: 0817643699 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors. Included in this chapter is an outline of the proof of McMullen's g-conjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly Cohen-Macaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory. Customer Reviews (2)
great book
This is a research monograph! |
13. Introduction to Algebraic Geometry and Commutative Algebra (IISc Lecture Notes Series) by Dilip P. Patil, Uwe Storch | |
Hardcover: 220
Pages
(2010-03-31)
list price: US$73.00 -- used & new: US$58.87 (price subject to change: see help) Asin: 9814304565 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses. |
14. Geometric And Combinatorial Aspects Of Commutative Algebra (Lecture Notes in Pure and Applied Mathematics) | |
Paperback: 391
Pages
(2001-03-06)
list price: US$219.95 -- used & new: US$12.00 (price subject to change: see help) Asin: 082470567X Canada | United Kingdom | Germany | France | Japan | |
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15. Commutative Algebra, Vol 2 by O. Zariski, Pierre Samuel | |
Hardcover: 432
Pages
(1976-03-29)
list price: US$89.95 -- used & new: US$38.94 (price subject to change: see help) Asin: 038790171X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Old writting style and no exercises
Not much to say, really. |
16. Operator Algebras: Theory of C*-Algebras and von Neumann Algebras (Encyclopaedia of Mathematical Sciences) by Bruce Blackadar | |
Paperback: 517
Pages
(2009-12-15)
list price: US$155.00 -- used & new: US$139.50 (price subject to change: see help) Asin: 3642066739 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail. |
17. Commutative Algebra: Chapters 1-7 by Nicolas Bourbaki | |
Paperback: 656
Pages
(1998-09-18)
list price: US$74.95 -- used & new: US$50.59 (price subject to change: see help) Asin: 3540642390 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
the next step |
18. Six Lectures on Commutative Algebra (Modern Birkhäuser Classics) | |
Paperback: 412
Pages
(2009-11-23)
list price: US$49.95 -- used & new: US$44.92 (price subject to change: see help) Asin: 3034603282 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (…). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (…) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "… this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "… since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH |
19. Trends in Commutative Algebra (Mathematical Sciences Research Institute Publications) | |
Paperback: 266
Pages
(2010-09-09)
list price: US$35.99 -- used & new: US$35.99 (price subject to change: see help) Asin: 0521168724 Canada | United Kingdom | Germany | France | Japan | |
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20. Linear Algebra over Commutative Rings (Pure and Applied Mathematics) by Mcdonald | |
Hardcover: 568
Pages
(1984-11-30)
list price: US$239.95 -- used & new: US$155.50 (price subject to change: see help) Asin: 0824771222 Canada | United Kingdom | Germany | France | Japan | |
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