- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
The Third Edition of this highly successful textbook for undergraduate and postgraduate students covers groups, rings, modules and fields, exhibits interplay of both Group and Field theory by means of Galois Theory and shows insolvability of a quintic, in general, by radicals. New to the third Edition: section on Semisimple Modules and Related Results.
Contents
Preface / Notations / PreliminariesRelation / The Integers / The Axiom of Choice / Countable and Uncountable Sets / Groups: Definitions and Examples / Subgroups / Cosets and Normal Subgroups / Homomorphisms / Normalizer, Centralizer and Class Equation / Symmetric Groups / Direct Products / Automorphisms / Sylow's Theorems / Applications of Sylow's Theorems / Series of Groups / Finite Abelian Groups / Groups of Small Order / Rings: Definitions and Examples / Ideals and Isomorphism Theorems / Direct Product of Rings / Rings of Polynomials / Fields of Fractions / Prime Ideals and Maximal Ideals / Factorization in Integral Domains / Noetherian Rings / Modules: Definitions and Examples / Module Homomorphisms and Quotient Modules / Direct Sums and Exact Sequences / Free Modules / Free Modules over PIDs / Finitely Generated Modules over PIDs / Projective and Injective Modules / Semisimple Modules / Fields: Field Extensions / Splitting Fields / Algebraically Closed Fields / Normal Extensions / Separable Extensions / Galois Theory / Galois Group of a Polynomial / Radical Extensions / Constructibility / Bibliography / Index.
