Algebra : A Graduate Course

This Book, Based On A First-year Graduate Course The Author Taught At The University Of Wisconsin, Contains More Than Enough Material For A Two Semester Graduate-level Abstract Algebra Course, Including Groups, Rings And Modules, Fields And Galois Theory, An Introduction To Algebraic Number Theory, And The Rudiments Of Algebraic Geometry. In Addition, There Are Some More Specialized Topics Not Usually Covered In Such A Course. These Include Transfer And Character Theory Of Finite Groups, Modules Over Artinian Rings, Modules Over Dedekind Domains, And Transcendental Field Extensions. This Book Could Be Used For Self Study As Well As For A Course Text, And So Full Details Of Almost All Proofs Are Included, With Nothing Being Relegated To The Chapter-end Problems. There Are, However, Hundreds Of Problems, Many Being Far From Trivial. The Book Attempts To Capture Some Of The Informality Of The Classroom, As Well As The Excitement The Author Felt When Taking The Corresponding Course As A Student.--book Jacket. Chapter 1. Definitions And Examples Of Groups Chapter 2. Subgroups And Cosets Chapter 3. Homomorphisms Chapter 4. Group Actions Chapter 5. The Sylow Theorems And $p$-groups Chapter 6. Permutation Groups Chapter 7. New Groups From Old Chapter 8. Solvable And Nilpotent Groups Chapter 9. Transfer Chapter 10. Operator Groups And Unique Decompositions Chapter 11. Module Theory Without Rings Chapter 12. Rings, Ideals, And Modules Chapter 13. Simple Modules And Primitive Rings Chapter 14. Artinian Rings And Projective Modules Chapter 15. An Introduction To Character Theory Chapter 16. Polynomial Rings, Pids, And Ufds Chapter 17. Field Extensions Chapter 18. Galois Theory Chapter 19. Separability And Inseparability Chapter 20. Cyclotomy And Geometric Constructions Chapter 21. Finite Fields Chapter 22. Roots, Radicals, And Real Numbers Chapter 23. Norms, Traces, And Discriminants Chapter 24. Transcendental Extensions Chapter 25. The Artin-schreier Theorem Chapter 26. Ideal Theory Chapter 27. Noetherian Rings Chapter 28. Integrality Chapter 29. Dedekind Domains Chapter 30. Algebraic Sets And The Nullstellensatz I. Martin Isaacs. Originally Published: Pacific Grove, Calif. : Brooks/cole, C1994. Includes Index. Includes Bibliographical References And Index. Presents an introduction to algebraic number theory, and the rudiments of algebraic geometry. This book includes such topics as transfer and character theory of finite groups, modules over artinian rings, modules over Dedekind domains, and transcendental field extensions.