Abstract 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.

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