| Algebra and its Applications | |
| Authors: S. T. Rizvi, M. A. Quadri, M. Ashraf | ISBN:
978-81-7319-419-1 |
About the book 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 | |
Key Features |
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Table of content 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 Audience Undergraduate students of Arts, Science and Engineering | |
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