Advanced Modern Algebra by Joseph J. Rotman
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About this book :-
This book is a graduate level textbook designed for students and researchers interested in abstract algebra. It cover the advanced topics as well and providing a comprehensive introduction to these subjects. It begins with a discussion of the cubic and quadratic 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 Grèobner bases. Next, non commutative 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 asderived 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.
Book Detail :-
This book has following details information.
Title:
Advanced Modern Algebra by Joseph J. Rotman by NA
Publisher:
Pearson College
Series:
FreeCompBooks
Year:
2003
Pages:
1040
Type:
PDF
Language:
English
ISBN-10 #:
0486453561
ISBN-13 #:
978-0130878687
Country:
Pakistan
License:
N\A
Get this book from Amazon
About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
1. Things Past
2. Groups I
3. Commutative Rings I
4. Fields
5. Groups II
6. Commutative Rings II
7. Modules and Categories
8. Algebras
9. Advanced Linear Algebra
10. Homology
11. Commutative Rings III
Appendix The Axiom of Choice and Zorn’s Lemma
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