000			02678cam a2200241 a 4500
005			20240316110010.0
008			091212s2010 riua b 001 0 eng
020			_a9780821847411
020			_a9781470419165
041			_aeng
082	0	0	_a512 _bRotA2
100	1		_aRotman, Joseph J.
245	1	0	_aAdvanced Modern Algebra / _cJoseph J. Rotman.
250			_a2nd Ed.
260			_aProvidence : _bAmerican Mathematical Society, _cc2010.
300			_axvi,1008p.
440			_aGraduate Studies in Mathematics _vVol.14
490	1		_a
505	0		_aGroups I -- Commutative rings I -- Galois theory -- Groups II -- Commutative rings II -- Rings -- Representative theory -- Advanced linear algebra -- Homology -- Commutative rings III.
520			_a"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	_aAlgebra
942			_cBK
999			_c5598 _d5598