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抽象代数基本教程 第7版PDF|Epub|txt|kindle电子书版本网盘下载
- (美)John B.Fraleigh 著
- 出版社： 北京世界图书出版公司
- ISBN：9787506292801
- 出版时间：2008
- 标注页数：520页
- 文件大小：47MB
- 文件页数：534页
- 主题词：抽象代数－教材－英文
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图书目录
0 Sets and Relations1
Ⅰ GROUPS AND SUBGROUPS11
1 Introduction and Examples11
2 Binary Operations20
3 Isomorphic Binary Structures28
4 Groups36
5 Subgroups49
6 Cyclic Groups59
7 Generating Sets and Cayley Digraphs68
Ⅱ PERMUTATIONS,COSETS,AND DIRECT PRODUCTS75
8 Groups of Permutations75
9 Orbits,Cycles,and the Alternating Groups87
10 Cosets and the Theorem of Lagrange96
11 Direct Products and Finitely Generated Abelian Groups104
12 Plane Isometries114
Ⅲ HOMOMORPHISMS AND FACTOR GROUPS125
13 Homomorphisms125
14 Factor Groups135
15 Factor-Group Computations and Simple Groups144
16 Group Action on a Set154
17 Applications of G-Sets to Counting161
Ⅳ RINGS AND FIELDS167
18 Rings and Fields167
19 Integral Domains177
20 Fermat's and Euler's Theorems184
21 The Field of Quotients of an Integral Domain190
22 Rings of Polynomials198
23 Factorization of Polynomials over a Field209
24 Noncommutative Examples220
25 Ordered Rings and Fields227
Ⅴ IDEALS AND FACTOR RINGS237
26 Homomorphisms and Factor Rings237
27 Prime and Maximal Ideals245
28 Gr？bner Bases for Ideals254
Ⅵ EXTENSION FIELDS265
29 Introduction to Extension Fields265
30 Vector Spaces274
31 Algebraic Extensions283
32 Geometric Constructions293
33 Finite Fields300
Ⅶ ADVANCED GROUP THEORY307
34 Isomorphism Theorems307
35 Series of Groups311
36 Sylow Theorems321
37 Applications of the Sylow Theory327
38 Free Abelian Groups333
39 Free Groups341
40 Group Presentations346
Ⅷ GROUPS IN TOPOLOGY355
41 Simplicial Complexes and Homology Groups355
42 Computations of Homology Groups363
43 More Homology Computations and Applications371
44 Homological Algebra379
Ⅸ FACTORIZATION389
45 Unique Factorization Domains389
46 Euclidean Domains401
47 Gaussian Integers and Multiplicative Norms407
Ⅹ AUTOMORPHISMS AND GALOIS THEORY415
48 Automorphisms of Fields415
49 The Isomorphism Extension Theorem424
50 Splitting Fields431
51 Separable Extensions436
52 Totally Inseparable Extensions444
53 Galois Theory448
54 Illustrations of Galois Theory457
55 Cyclotomic Extensions464
56 Insolvability of the Quintic470
Appendix:Matrix Algebra477
Bibliography483
Notations487
Answers to Odd-Numbered Exercises Not Asking for Definitions or Proofs491
Index513