Abstract Algebra, 3rd Edition

Preliminaries.

PART I: GROUP THEORY.

Chapter 1. Introduction to Groups.

Chapter 2. Subgroups.

Chapter 3. Quotient Group and Homomorphisms.

Chapter 4. Group Actions.

Chapter 5. Direct and Semidirect Products and Abelian Groups.

Chapter 6. Further Topics in Group Theory.

PART II: RING THEORY.

Chapter 7. Introduction to Rings.

Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.

Chapter 9. Polynomial Rings.

PART III: MODULES AND VECTOR SPACES.

Chapter 10. Introduction to Module Theory.

Chapter 11. Vector Spaces.

Chapter 12. Modules over Principal Ideal Domains.

PART IV: FIELD THEORY AND GALOIS THEORY.

Chapter 13. Field Theory.

Chapter 14. Galois Theory.

PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA.

Chapter 15. Commutative Rings and Algebraic Geometry.

Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.

Chapter 17. Introduction to Homological Algebra and Group Cohomology.

PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS.

Chapter 18. Representation Theory and Character Theory.

Chapter 19. Examples and Applications of Character Theory.

Appendix I: Cartesian Products and Zorn's Lemma.

Appendix II: Category Theory.

Index.