抽象代数基础教程 第7版

◎内容简介

本书是一部深入介绍抽象代数的入门书籍，被众多读者奉为经典。本书旨在让读者尽可能多地了解群、环和域理论的相关知识，尤其强调对代数结构本质的理解。为了便于学习，全书分成了很多的小章节，本书特色之一是基础部分内容详实，讲解充分，给读者讲解每个定义、定理的来龙去脉，为读者打下扎实的基础，对于读者进一步学习更深的代数大有助益。为了满足更多读者的需求，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。作者的风格是以一种自然易懂的方式来教授内容，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。书后附有不少习题，有助于加深学生对内容的理解。读者可以扫描世图版全书最后一页上的二维码，加群获取本书完整的习题解答。

◎作者简介

约翰·弗雷利（John B. Fraleigh）是美国罗德岛大学数学与应用数学科学系的荣休教授，一生致力于数学教育，获得了诸多赞誉，罗德岛大学还设立了以他名字命名的奖学金。他出版过多部有影响力的数学教材，《抽象代数基础教程》是其代表作之一，多年来一直被奉为经典，长销不衰。

◎图书目录

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