000			03063cam a2200325 a 4500
001			16020657
005			20230114171232.0
008			091212s2010 riua b 001 0 eng
010			_a 2009052217
015			_aGBB089720 _2bnb
016	7		_a015611457 _2Uk
020			_a9780821847411 (alk. paper)
020			_a9781470419165
020			_a0821847414 (alk. paper)
035			_a(OCoLC)ocn489257921
050	0	0	_aQA154.3 _b.R68 2010
082	0	0	_a512 _222 _bROT/A
100	1		_aRotman, Joseph J., _d1934- _916666
245	1	0	_aAdvanced modern algebra / _cJoseph J. Rotman.
250			_a2nd ed.
260			_aProvidence, R.I. : _bAmerican Mathematical Society, _cc2010.
300			_axvi, 1008 p. : _bill. ; _c27 cm.
490	1		_aGraduate studies in mathematics ; _vv. 114
504			_aIncludes bibliographical references and index.
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. _9374
830		0	_aGraduate studies in mathematics ; _vv. 114. _916667
942			_2ddc _cGB _07
999			_c823 _d823