Abstract Algebra¶
Textbook Information¶
John B. Fraleigh - A First Course in Abstract Algebra, Seventh Edition
Table of Contents¶
Ch 0. Sets and Relations¶
Ch 1. Groups and Subgroups¶
- 1. Introduction and Examples
- 2. Binary Operations
- 3. Isomorphic Binary Structures
- 4. Groups
- 5. Subgroups
- 6. Cyclic Groups
- 7. Generating Sets and Cayley Digraphs
Ch 2. Permutations, Cosets, and Direct Products¶
- 8. Groups of Permutations
- 9. Orbits, Cycles, and the Alternating Groups
- 10. Cosets and the Theorem of Lagrange
- 11. Direct Products and Finitely Generated Abelian Groups
- 12. Plane Isometries
Ch 3. Homomorphisms and Factor Groups¶
- 13. Homomorphisms
- 14. Factor Groups
- 15. Factor-Group Computations and Simple Groups
- 16. Group Action on a Set
- 17. Applications of G-Sets to Counting
Ch 4. Rings and Fields¶
- 18. Rings and Fields
- 19. Integral Domains
- 20. Fermat's and Euler's Theorems
- 21. The Field of Quotients of an Integral Domain
- 22. Rings of Polynomials
- 23. Factorization of Polynomials over a Field
- 24. Noncommutative Examples
- 25. Ordered Rings and Fields
Ch 5. Ideals and Factor Rings¶
- [26. Homomorphisms and Factor Rings]
- [27. Prime and Maximal Ideals]
- [28. Grobner Bases for Ideals]
Ch 6. Extension Fields¶
- [29. Introduction to Extension Fields]
- [30. Vector Spaces]
- [31. Algebraic Extensions]
- [32. Geometric Constructions]
- [33. Finite Fields]
Ch 7. Advanced Group Theory¶
- [34. Isomorphism Theorems]
- [35. Series of Groups]
- [36. Sylow Theorems]
- [37. Applications of the Sylow Theory]
- [38. Free Abelian Groups]
- [39. Free Groups]
- [40. Group Presentations]
Ch 9. Factorization¶
- [45. Unique Factorization Domains]
- [46. Euclidean Domains]
- [47. Gaussian Integers and Multiplicative Norms]
Ch 10. Automorphisms and Galois Theory¶
- [48. Automorphisms of Fields]
- [49. The Isomorphism Extension Theorem]
- [50. Splitting Fields]
- [51. Separable Extensions]
- [52. Totally Inseparable Extensions]
- [53. Galois Theory]
- [54. Illustrations of Galois Theory]
- [55. Cyclotomic Extensions]
- [56. Insolvability of the Quintic]
Appendix¶
- [A. Matrix Algebra]