This book highlights the interactions of various branches of algebra such as: Rough Groups, Normal Semi-Groups, Quasi Baer-Rings, Exchange Rings, CS Rings, Near Rings, Jordan and Lie Homomorphisms in Rings, Derivations, Serial Modules, Pseudo M-Injective Modules, Jordan Algebras, Coding Theory and Category Theory

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

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