Abstract AlgebraAn introductory text with sections on group theory, ring theory, modules and vector spaces, field theory and galois theory, an introduction to the representation theory of finite groups, and an introduction to commutative rings, algebraic geometry, and homological algebra. Exercises range from routine computations to fairly sophisticated theoretical ones. This second edition provides greater flexibility instructors wishing to use the text for an introductory undergraduate course and for topics courses at the graduate level. Annotation copyrighted by Book News, Inc., Portland, OR |
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a₁ abelian group algebraic set automorphism basis canonical form coefficients cohomology commutative ring conjugacy classes conjugate contains Corollary corresponding cosets cyclic group decomposition Deduce defined definition degree denote determine direct product direct sum element of order equation equivalent Euclidean example Exercise field F finite group fixed follows functions functor Galois group group G group of order hence identity induced injective integer integral domain invariant factors inverse irreducible characters isomorphic kernel Lemma Let F Let G linear transformation matrix maximal ideal minimal polynomial module morphism multiplication nilpotent Noetherian nonzero element normal subgroup permutation prime ideal Proposition Prove R-module R-module homomorphism 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 p-subgroup symmetric tensor Theorem vector space Z/nZ zero