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1. Set Theory and Metric Spaces (AMS Chelsea Publishing) by Irving Kaplansky | |
Hardcover: 140
Pages
(2001-05-01)
list price: US$30.00 -- used & new: US$27.63 (price subject to change: see help) Asin: 0821826948 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Book of Rare Beauty
Extremely helpful!
Extremely helpful! |
2. Linear Algebra and Geometry: A Second Course (Dover Books on Mathematics) by Irving Kaplansky | |
Paperback: 160
Pages
(2003-08-15)
list price: US$12.95 -- used & new: US$6.99 (price subject to change: see help) Asin: 0486432335 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition. |
3. Infinite Abelian Groups. by Irving, Kaplansky | |
Paperback:
Pages
(1969-01)
list price: US$4.00 Isbn: 047208500X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
A compact and Accessible Introduction to Infinite Group Theory |
4. Lie Algebras and Locally Compact Groups (Chicago Lectures in Mathematics) by Irving Kaplansky | |
Paperback: 155
Pages
(1995-02-27)
list price: US$32.00 -- used & new: US$28.80 (price subject to change: see help) Asin: 0226424537 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
5. Selected Papers and other Writings by Irving Kaplansky | |
Hardcover: 280
Pages
(1995-04-13)
list price: US$104.00 -- used & new: US$78.06 (price subject to change: see help) Asin: 0387944060 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
6. Fields and Rings (Chicago Lectures in Mathematics) by Irving Kaplansky | |
Paperback: 207
Pages
(1995-02-27)
list price: US$30.00 -- used & new: US$26.00 (price subject to change: see help) Asin: 0226424510 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Pretty good The author begins the discussion with field extensions. One can view a field L containing another field K as a vector space over K, and the dimension of L (as a vector space) is then called the 'dimension' of L over K. If one considers a subfield K of a field M, and an additional element u in M, then there is a smallest subfield of M containing K and u. Calling this field K(u), u can be either transcendental or algebraic over K. The author then proves some elementary properties of the field K(u), showing the existence of an irreducible polynomial for u over K. This then motivates him to call a field L containing K 'algebraic' over K if every element of L is algebraic over K. Otherwise L is called 'transcendental' over K. The dimension of K(u) over K is called the degree of u over K. Finding the degree of u can be done by finding the irreducible polynomial for u. The author also proves the arithmetic relation between the dimensions of towers of fields, and this allows him to prove the famous results on the impossibility of ruler and compass constructions. For a field L that lies between fields K and M the author studies the 'stability' of L over K, meaning that every automorphism of M/K sends L into itself. The correspondence between stable fields and normal subgroups of the Galois group of M/K is proven. Splitting fields are introduced as devices to obtain fields that are normal over a given field. A criterion for a splitting field that does not involve polynomials is proven, and the author gives tools that deal with fields of non-zero characteristic, these tools motivating the definition of separability. Splitting fields are normal in characteristic 0, but one must add separability for the same to hold in characteristic p. The unsolvability of the quintic is shown via a discussion on radical extensions of fields. For a field K of characteristic 0, and for a field L lying between K and another field M, where M is a radical extension of K, the author proves in detail that the Galois group of L/K will be solvable. Then if one has a polynomial with coefficients in K, then the Galois group of this polynomial is defined to be the Galois group of a splitting field of the polynomial over K. The Galois group of the polynomial is thought of as a group of permutations of the roots of the polynomial. The author then proves that if K has characteristic 0 and L is a radical extension of K which contains a root of the polynomial, then the Galois group of the polynomial over K is solvable. Those readers involved in cryptography will find a discussion of finite fields in Part 1. The author's goal is to find the finite fields and determine their structure. He first proves that every nth power of a prime number p will yield a field with p^n elements. The author shows that the Galois theory of finite fields is simple by proving that if K is a finite field contained in another finite field L, then L is normal over K and the Galois group of L/K is cyclic. The author also shows how the Galois group of an equation can be found explicitly for the cubic and quartic equations. He shows first that for the Galois group of a separable irreducible cubic over a field K is either the alternating group A(3) or the symmetric group S(3). If the characteristic of K is not equal to 2, then it is A(3) if and only if the discriminant is a square in K. For a separable irreducible quartic over K, then for the degree over K of the splitting field of the resolvent cubic of this polynomial, the Galois group is S(4) if the degree is 6, A(4) if the degree is 3, V (a particular normal subgroup of S(4)) if the degree is 1, and either the group of order 8 or cyclic of order 4 if the degree is 2. Also in part 1, the author studies the reducibility of an equation of the form x^n -a over an arbitrary field. He addresses this reducibility by first proving that one only need be concerned for the case where n is a prime power. Then if p is prime, and "a " does not have any pth root in the field K, then if the prime is odd, then the equation is irreducible over K for any n. If p = 2 and the characteristic of K is 2, then the equation is irreducible over K for any n. If p = 2, n is greater than or equal to 2, and the characteristic of K is not 2, then the equation is irreducible over K if and only if -4a is not a fourth power in K. The author also proves the fundamental theorem of algebra using Galois theory. He does this by first showing that if every extension of K has degree divisible by a prime p, then every extension of K has degree a power of p. ... Read more |
7. Linear Algebra and Geometry: Second Course by Irving Kaplansky | |
Hardcover: 143
Pages
(1974-06)
list price: US$12.95 -- used & new: US$67.44 (price subject to change: see help) Asin: 0828402795 Canada | United Kingdom | Germany | France | Japan | |
8. Commutative rings by Irving Kaplansky | |
Hardcover: 180
Pages
(1970)
Asin: B0006C2PIC Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
Good but antiquated. |
9. An Introduction to Differential Algebra (Actualites Scientifiques Et Industrielles, 1251) by Irving Kaplansky | |
Paperback: 62
Pages
(1957)
Asin: B000P26CKA Canada | United Kingdom | Germany | France | Japan | |
10. Rings of operators (Mathematics lecture note series) by Irving Kaplansky | |
Paperback: 151
Pages
(1968)
Asin: B0006BTSDS Canada | United Kingdom | Germany | France | Japan | |
11. Chicago Lectures in Mathematics: Fields and Rings by Irving Kaplansky | |
Paperback:
Pages
(1970)
Asin: B002JYDNFE Canada | United Kingdom | Germany | France | Japan | |
12. FIRLDS AND RINGS (CHICAGO LECTURES IN MATHEMATICS) by Irving Kaplansky | |
Paperback:
Pages
(1969)
Asin: B000RDUB0O Canada | United Kingdom | Germany | France | Japan | |
13. Some Aspects of Analysis and Probability. (Surveys in Applied Mathematics, IV) by Irving, Marshall Hall, Jr., Edwin Hewitt, and Robert Fortet. Kaplansky | |
Hardcover: 243
Pages
(1958)
Asin: B000Q9T0DI Canada | United Kingdom | Germany | France | Japan | |
14. The theory of rings: Lectures delivered ... University of California at Los Angeles, Spring 1955 by Irving Kaplansky | |
Unbound: 79
Pages
(1955)
Asin: B0007J1AYY Canada | United Kingdom | Germany | France | Japan | |
15. Rings of Operators. [Typed] Notes Prepared by S. Berbarian with an Appendix by R. Blattner. Mathematics 337A, Summer 1955. 53 Pages by Irving Kaplansky | |
Paperback: 53
Pages
(1955)
Asin: B00292G1UU Canada | United Kingdom | Germany | France | Japan | |
16. Linear Algebra and Geometry by Irving Kaplansky | |
Hardcover: 139
Pages
(1969)
Asin: B001QUK3LE Canada | United Kingdom | Germany | France | Japan | |
17. RINGS OF OPERATORS by IRVING KAPLANSKY | |
Hardcover:
Pages
(1968-01-01)
Asin: B0010ZN9N4 Canada | United Kingdom | Germany | France | Japan | |
18. Proceedings Of The American Mathematical Society: Vol.10, No.5; October, 1959 by R.P.; Kaplansky, Irving;Halmos, P.R.; Samelson, Hans: (Ed.s) Boas | |
Paperback:
Pages
(1959)
Asin: B000KGDZ9C Canada | United Kingdom | Germany | France | Japan | |
19. The theory of fields: Notes for Mathematics 322 by Irving Kaplansky | |
Unknown Binding:
Pages
(1965)
Asin: B0007F57I8 Canada | United Kingdom | Germany | France | Japan | |
20. Infinite Abelian Groups by Irving Kaplansky | |
Paperback:
Pages
(1962)
Asin: B0020AUXVE Canada | United Kingdom | Germany | France | Japan | |
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