A First Course in Abstract Algebra

✍ Scribed by John B. Fraleigh, Neal E. Brand

• Publisher: Pearson
• Year: 2021
• Tongue: English
• Leaves: 442
• Edition: 8
• Category: Library

✦ Table of Contents

Title
Contents
Instructor's Preface
Student’s Preface
0. Sets and Relations
I. Groups and Subgroups
1. Binary Operations
2. Groups
3. Abelian Examples
4. Nonabelian Examples
5. Subgroups
6. Cyclic Groups
7. Generating Sets and Cayley Digraphs
II. Structure of Groups
8. Groups of Permutations
9. Finitely Generated Abelian Groups
10. Cosets and the Theorem of Lagrange
11. Plane Isometries
III. Homomorphisms and Factor Groups
12. Factor Groups
13. Factor-Group Computations and Simple Groups
14. Group Action on a Set
15. Applications of G-Sets to Counting
IV. Advanced Group Theory
16. Isomorphism Theorems
17. Sylow Theorems
18. Series of Groups
19. Free Abelian Groups
20. Free Groups
21. Group Presentations
V. Rings and Fields
22. Rings and Fields
23. Integral Domains
24. Fermat’s and Euler’s Theorems
25. Encryption
VI. Constructing Rings and Fields
26. The Field of Quotients of an Integral Domain
27. Rings of Polynomials
28. Factorization of Polynomials over a Field
29. Algebraic Coding Theory
30. Homomorphisms and Factor Rings
31. Prime and Maximal Ideals
32. Noncommutative Examples
VII. Commutative Algebra
33. Vector Spaces
34. Unique Factorization Domains
35. Euclidean Domains
36. Number Theory
37. Algebraic Geometry
38. Gröbner Bases for Ideals
VIII. Extension Fields
39. Introduction to Extension Fields
40. Algebraic Extensions
41. Geometric Constructions
42. Finite Fields
IX. Galois Theory
43. Introduction to Galois Theory
44. Splitting Fields
45. Separable Extensions
46. Galois Theory
47. Illustrations of Galois Theory
48. Cyclotomic Extensions
49. Insolvability of the Quintic
Appendix: Matrix Algebra
Bibliography
Notations
Answers to Odd-Numbered Exercises Not Asking for Definitions or Proofs
Index