A Book of Abstract Algebra

A Book of Abstract Algebra, Second Edition (1982)

PREFACE

Chapter 1. WHY ABSTRACT ALGEBRA?

Chapter 2. OPERATIONS

Chapter 3. THE DEFINITION OF GROUPS

Chapter 4. ELEMENTARY PROPERTIES OF GROUPS

Chapter 5. SUBGROUPS

Chapter 6. FUNCTIONS

Chapter 7. GROUPS OF PERMUTATIONS

Chapter 8. PERMUTATIONS OF A FINITE SET

Chapter 9. ISOMORPHISM

Chapter 10. ORDER OF GROUP ELEMENTS

Chapter 11. CYCLIC GROUPS

Chapter 12. PARTITIONS AND EQUIVALENCE RELATIONS

Chapter 13. COUNTING COSETS

Chapter 14. HOMOMORPHISMS

Chapter 15. QUOTIENT GROUPS

Chapter 16. THE FUNDAMENTAL HOMOMORPHISM THEOREM

Chapter 17. RINGS: DEFINITIONS AND ELEMENTARY PROPERTIES

Chapter 18. IDEALS AND HOMOMORPHISMS

Chapter 19. QUOTIENT RINGS

Chapter 20. INTEGRAL DOMAINS

Chapter 21. THE INTEGERS

Chapter 22. FACTORING INTO PRIMES

Chapter 23. ELEMENTS OF NUMBER THEORY (OPTIONAL)

Chapter 24. RINGS OF POLYNOMIALS

Chapter 25. FACTORING POLYNOMIALS

Chapter 26. SUBSTITUTION IN POLYNOMIALS

Chapter 27. EXTENSIONS OF FIELDS

Chapter 28. VECTOR SPACES

Chapter 29. DEGREES OF FIELD EXTENSIONS

Chapter 30. RULER AND COMPASS

Chapter 31. GALOIS THEORY: PREAMBLE

Chapter 32. GALOIS THEORY: THE HEART OF THE MATTER

Chapter 33. SOLVING EQUATIONS BY RADICALS

APPENDIX A. REVIEW OF SET THEORY

APPENDIX B. REVIEW OF THE INTEGERS

APPENDIX C. REVIEW OF MATHEMATICAL INDUCTION

ANSWERS TO SELECTED EXERCISES