A First Course in Abstract Algebra, 8th edition

  • John B. Fraleigh, 
  • Neal Brand

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Overview

A First Course in Abstract Algebra is an in-depth introduction ideal for future graduate students, future high school teachers, and students who intend to work in industry.  


Published by Pearson (May 1st 2020) - Copyright © 2021

ISBN-13: 9780135859759

Subject: Advanced Math

Category: Abstract Algebra

Table of contents

Instructor's Preface
Dependence Chart
Student's Preface
0. Sets and Relations

I. GROUPS AND SUBGROUPS
1. Binary Operations
2. Groups
3. Abelian Groups
4. Nonabelian Examples
5. Subgroups
6. Cyclic Groups
7. Generating Sets and Cayley Digraphs

II. STRUCTURE OF GROUPS
8. Groups and 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. Groups Actions 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 and Polynomials
28. Factorization of Polynomials over Fields
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 Basis 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

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