description: Highlighting the interactions of various branches of algebra, this informative volume delves into the key areas, like Rough Groups, Normal Semi-Groups, Quasi Baer-Rings and Exchange rings, alongside a great many others.Table of Contents• Preface• Notations• Preliminaries• Sets and Mappings• Equivalence relation• The Integers• The Axiom of Choice• Countable and Uncountable Sets• Groups• Definitions and Examples• Subgroups• Cosets and Normal Subgroups• Homomorphisms• Normalizer, Centerlizer 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• Fields• Field Extensions• Splitting Fields• Algebraically Closed Fields• Normal Extensions• Separable Extensions• Galois Theory• Galois Group of a Polynomial• Radiacal Extensions• Constructibility• Bibliography• Index
language: English
title: Algebra and its Applications
titlecomplete: Algebra and its Applications
publisher: Alpha Science