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The second edition of this textbook on Abstract Algebra continues to provide a fully self-contained treatment of the fundamental concepts of the subject, taking care to introduce each notion with sufficient number of solved examples that would help readers understand and master the theories presented. A fine collection of exercises enriches each chapter, challenging the readers to check their progress in understanding the results and methods of the discipline, as well as motivating them for more algebra. The book’s writing style is intended to foster students–instructor discussion. A unique learning feature of the text is that each concept in abstract algebra is treated in a separate chapter, taking care of the continuity of the subject matter for easy comprehension by the students. Besides presenting the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them, the second edition has been enriched by the inclusion of a new chapter on matrices and their properties and some special subsets of matrices. In addition, proofs of some of the theorems have been revised and some exercises have been changed into solved examples. The book provides a pedagogical introduction to the topics of abstract algebra and is especially suited for an undergraduate course, though it will be of equal value to the postgraduate students of the subject. About The Author I. H. SHETH Ph.D., is formerly from the Department of Mathematics, University School of Sciences, Gujarat University. He has over 35 years teaching experience in abstract algebra, linear algebra and real analysis both at the undergraduate and postgraduate levels. Table Of Contents Preface Preface to First Edition Note to the Student Notations Part I: PRELIMINARIES 1. SET THEORY 2. RELATIONS 3. MAPPINGS 4. MATRICES 5. BINARY OPERATIONS 6. INTEGERS Part II: GROUP THEORY 7. GROUPS 8. SUBGROUPS 9. PERMUTATIONS 10. NORMAL SUBGROUPS 11. ISOMORPHISM OF GROUPS 12. CYCLIC GROUPS 13. HOMOMORPHISM: 1 Part III: RING THEORY 14. RINGS 15. INTEGRAL DOMAINS 16. IDEALS: 1 17. HOMOMORPHISM: 2 18. FIELDS 19. POLYNOMIALS 20. IDEALS: 2 21. FINITE FIELDS 22. UNIQUE FACTORIZATION DOMAIN AND EUCLIDEAN RING Appendices A: De Moivre’s Theorem B: Three Famous Problems Supplementary Problems References Index