Topics in Abstract Algebra

By: M K Sen, Shamik Ghosh, Parthasarathi Mukhopadhyay & Sunil Kumar Maity (Authors)

Price: $18.90

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About the Book Replete with thought-provoking examples and worked-out exercises, this third edition of Topics in Abstract Algebra is designed in accordance with the new Choice Based Credit System (CBCS) syllabus of Abstract Algebra and Advanced Abstract Algebra prescribed by UGC for all Indian universities at the UG Honours/Advanced level. Students appearing for competitive entrance examinations such as NET, JAM, ISI, IISc., TIFR, NBHM, GATE, SET or MCA will benefit immensely from the carefully selected Solved Problems, about a hundred of which (of MCQ type) have been newly added to the present edition. Interesting insights to the history of mathematics and mathematicians are also provided in the course of discussion to enable the readers understand the concepts in the right perspective.Table of Contents About the Authors Preface to the Third Edition Preface to the First Edition 1. Preliminaries 1.1 Sets 1.2 Relations 1.3 Congruous Relation 1.4 Functions 1.5 Binary Operations 2. Integers 2.1 Divisibility 2.2 Mathematical Induction 2.3 Prime Numbers 2.4 Linear Diophantine Equations 2.5 Arithmetic Functions 2.6 More on Congruence 3. Groups 3.1 Elementary Properties 4. Permutation Groups 4.1 Permutation Group 5. Subgroups 5.1 Subgroups 5.2 Cyclic Groups 5.3 Cosets and Lagrange’s Theorem 5.4 Normal Subgroups and Quotient Groups 6. Homomorphisms of Groups 6.1 Homomorphisms 6.2 Isomorphism Theorems 7. Direct Product of Groups 7.1 Direct Product 8. Symmetry 8.1 Isometry 8.2 Four Isometries of the Plane 8.3 Group of Symmetries 9. Finite Abelian Groups 9.1 Finite Abelian Groups 10. Sylow Theorems 10.1 Group Actions 10.2 Class Equation and Cauchy’s Theorem 10.3 Sylow Theorems 11. Simple Groups 11.1 Simple Groups 12. Rings 12.1 Elementary Properties 12.2 Integral Domains, Division Rings and Fields 12.3 Subrings and Subfields 12.4 Regular Rings 13. Ideals and Homomorphisms of Rings 13.1 Ideals and Quotient Rings 13.2 Homomorphisms 13.3 Maximal ideals and Prime ideals 13.4 Embedding of Rings 14. Factorization in Integer Domains 14.1 Factorization Domain 14.2 Euclidean Domain 15. Polynomial Rings 15.1 Ring of Polynomials 15.2 Irreducibility of Polynomials Appendices Bibliography Answers Index. Printed Pages: 548

Title: Topics in Abstract Algebra

Author Name: M K Sen, Shamik Ghosh, Parthasarathi Mukhopadhyay & Sunil Kumar Maity (Authors)

Categories: Mathematics, India,

Edition: Third Edition

Publisher: New Delhi, Universities Press/Orient BlackSwan: 2019

ISBN: 9789386235701

Binding: Softcover

Book Condition: New

Seller ID: 1202481

Keywords: Topics in Abstract Algebra M K Sen, Shamik Ghosh, Parthasarathi Mukhopadhyay & Sunil Kumar Maity (Authors)