本书是一部深入介绍抽象代数的入门书籍，被许多读者奉为经典。本书假定读者了解了微积分和线性代数，旨在让读者尽可能多的了解群、环、以及域理论的有关知识。本书特色之一是基础部分内容详实，讲解扎实，可以为读者打下良好的基础，对于读者更进一步的学习代数大有助益。为了满足更多读者的要求，本书还包含了很多有关拓扑中的同调群和同调群的计算以加深对因子群的理解。书中内容浅显易懂，理论阐述清晰，条理分明，且大都以例子和练习的形式，便于直观了解。为了将同调群讲述的更加清楚，本书在第6版的基础上减少了自动机、二进制线性。
Preface
0. Sets and Relations
I. GROUPS AND SUBGROUPS
1. Introduction and Examples
2. Binary Operations
3. Isomorphic Binary Structures
4. Groups
5. Subgroups
6. Cyclic Groups
7. Generators and Cayley Digraphs
II. 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
III. 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
IV. 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
V. IDEALS AND FACTOR RINGS
26. Homomorphisms and Factor Rings
27. Prime and Maximal Ideas
28. Groebner Bases for Ideals
VI. EXTENSION FIELDS
29. Introduction to Extension Fields
30. Vector Spaces
31. Algebraic Extensions
32. Geometric Constructions
33. Finite Fields
VII. 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
VIII. AUTOMORPHISMS AND GALOIS THEORY
41. Automorphisms of Fields
42. The Isomorphism Extension Theorem
43. Splitting Fields
44. Separable Extensions
45. Totally Inseparable Extensions
46. Galois Theory
47. Illustrations of Galois Theory
48. Cyclotomic Extensions
49. Insolvability of the Quintic
Appendix: Matrix Algebra
Bibliography
Notations
Index
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