Abstract AlgebraCovering such material as tensor products, commutative rings, algebraic number theory and introductory algebraic geometry, this work includes exercises ranging in scope from routine to fairly sophisticated, including exploration of important theoretical or computational techniques. |
Contents
GROUP THEORY | 13 |
Subgroups | 47 |
Quotient Groups and Homomorphisms | 74 |
Copyright | |
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a₁ abelian group algebraic set automorphism basis bijection canonical form coefficients cohomology commutative ring conjugacy classes conjugate contains Corollary 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 left cosets Lemma Let F Let G linear transformation matrix maximal ideal minimal polynomial module morphism multiplication nilpotent Noetherian nonzero element normal subgroup permutation prime ideal Principal 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 tensor Theorem vector space Z/nZ zero