Abstract algebraThe book carefully develops the theory of different algebraic structures, beginning from basic definitions to some indepth results, using numerous examples and exercises throughout to aid the reader's understanding. This edition includes substantial new material in areas that include: tensor products, commutative rings, algebraic number theory and introductory algebraic geometry. Also, includes rings of algebraic integers, semidirect products and splitting of extensions, criteria for the solvability. of a quintic, and Dedekind Domains. 
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Review: Abstract Algebra
User Review  Waffles  GoodreadsIt's a math text, so I didn't enjoy reading it, but it is a good comprehensive overview of algebra. I'm glad this was the text for my algebra sequence. Read full review
Review: Abstract Algebra
User Review  Natalya  GoodreadsEww, I have bad memories of Professor Shariari now. Read full review
Contents
GROUP THEORY  13 
Subgroups  47 
Quotient Groups and Homomorphisms  74 
Copyright  
19 other sections not shown
Common terms and phrases
abelian group automorphism basis bijection called coefficients cohomology commutative ring completes the proof conjugacy classes conjugate contains Corollary corresponding cosets cyclic group decomposition Deduce defined definition denote determine direct product direct sum divides element of order elementary divisors elements of G equation equivalent example field F finite group follows functions functor g e G Galois extension Galois group gives group G group of order hence identity induced injective integral domain invariant factors inverse irreducible characters isomorphic kernel Lemma Let G linear transformation matrix maximal ideal minimal polynomial module homomorphism morphism multiplication n x n nilpotent Noetherian nonzero element normal subgroup Note particular permutation prime ideal Principal Ideal Proposition Prove representation ring homomorphism roots of unity Section short exact sequence Show simple group Spec splitting field subfield subgroup of G submodule subring subset Suppose surjective Sylow psubgroup symmetric Theorem vector space Zmodule Z/nZ zero