For one-semester or two-semester undergraduate courses in Abstract Algebra.
This new edition has been completely rewritten. The four chapters from the first edition are expanded, from 257 pages in first edition to 384 in the second. Two new chapters have been added: the first 3 chapters are a text for a one-semester course; the last 3 chapters are a text for a second semester. The new Chapter 5, Groups II, contains the fundamental theorem of finite abelian groups, the Sylow theorems, the Jordan-Holder theorem and solvable groups, and presentations of groups (including a careful construction of free groups). The new Chapter 6, Commutative Rings II, introduces prime and maximal ideals, unique factorization in polynomial rings in several variables, noetherian rings and the Hilbert basis theorem, affine varieties (including a proof of Hilbert's Nullstellensatz over the complex numbers and irreducible components), and Grobner bases, including the generalized division algorithm and Buchberger's algorithm.
- ISBN10 0130115843
- ISBN13 9780130115843
- Publish Date 17 April 2000 (first published 5 December 1995)
- Publish Status Out of Print
- Out of Print 17 June 2010
- Publish Country US
- Imprint Pearson
- Edition 2nd edition
- Format Hardcover
- Pages 531
- Language English