Advanced Modern Algebra / (Record no. 5598)

MARC details
000 -LEADER
fixed length control field 02678cam a2200241 a 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240316110010.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 091212s2010 riua b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9780821847411
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781470419165
041 ## - LANGUAGE CODE
Language code of text/sound track or separate title eng
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512
Item number RotA2
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name Rotman, Joseph J.
245 10 - TITLE STATEMENT
Title Advanced Modern Algebra /
Statement of responsibility, etc Joseph J. Rotman.
250 ## - EDITION STATEMENT
Edition statement 2nd Ed.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication Providence :
Name of publisher American Mathematical Society,
Year of publication c2010.
300 ## - PHYSICAL DESCRIPTION
Number of Pages xvi,1008p.
440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Graduate Studies in Mathematics
Volume number/sequential designation Vol.14
490 1# - SERIES STATEMENT
Series statement
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Groups I -- Commutative rings I -- Galois theory -- Groups II -- Commutative rings II -- Rings -- Representative theory -- Advanced linear algebra -- Homology -- Commutative rings III.
520 ## - SUMMARY, ETC.
Summary, etc "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 topics 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 Gröbner 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."--Publisher's description.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Algebra
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Books
Holdings
Withdrawn status Lost status Damaged status Collection code Home library Current library Shelving location Date acquired Source of acquisition Purchase Price Bill number Full call number Accession Number Print Price Bill Date/Price effective from Koha item type
      Mathematics Indian Institute of Technology Tirupati Indian Institute of Technology Tirupati General Stacks 14/03/2024 Gifted 0.00 Free 512 RotA2 10295 2950.00 14/03/2024 Books