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Advanced Modern Algebra - 2nd edition

Advanced Modern Algebra (ISBN10: 0821847414; ISBN13: 9780821847411)
ISBN13: 978-0821847411
ISBN10: 0821847414

This new edition begins with a discussion of the cubic & quartic equations, which leads into permutations, group theory & Galois theory. The study of groups includes finite abelian groups, Sylow theorems, simplicity of projective unimodular groups, free groups & presentations, & the Nielsen-Schreier theorem.

Edition/Copyright: 2ND 11
Cover: Hardback
Publisher: American Mathematical Society
Published: 09/09/2010
International: No



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Brand new. We distribute directly for the publisher. This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topi ...show morecs as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free).The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gr??bner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra.Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic $K$-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization. ...show less
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2010 Hardback NEAR FINE 9780821847411 Hardback, This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. *****PLEASE NOTE: This item is shi ...show morepping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** ...show less
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