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离散赋值环上的模PDF|Epub|txt|kindle电子书版本网盘下载
- （俄罗斯）P.A.克雷洛夫（piotra.krylov），A.A.图根巴夫（askara.tuganbaev）著 著
- 出版社： 北京世界图书出版公司
- ISBN：9787519214760
- 出版时间：2016
- 标注页数：357页
- 文件大小：53MB
- 文件页数：368页
- 主题词：离散赋值－模－英文
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图书目录
1 Preliminaries1
1 Some definitions and notation1
2 Endomorphisms and homomorphisms of modules7
3 Discrete valuation domains16
4 Primary notions of module theory31
2 Basic facts46
5 Free modules46
6 Divisible modules49
7 Pure submodules55
8 Direct sums of cyclic modules60
9 Basic submodules65
10 Pure-projective and pure-injective modules72
11 Complete modules77
3 Endomorphism rings of divisible and complete modules86
12 Examples of endomorphism rings87
13 Harrison-Matlis equivalence89
14 Jacobson radical94
15 Galois correspondences105
4 Representation of rings by endomorphism rings116
16 Finite topology117
17 Ideal of finite endomorphisms119
18 Characterization theorems for endomorphism rings of torsion-free modules126
19 Realization theorems for endomorphism rings of torsion-free modules134
20 Essentially indecomposable modules141
21 Cotorsion modules and cotorsion hulls146
22 Embedding of category of torsion-free modules in category of mixed modules156
5 Torsion-free modules166
23 Elementary properties of torsion-free modules167
24 Category of quasihomomorphisms170
25 Purely indecomposable and copurely indecomposable modules180
26 Indecomposable modules over Nagata valuation domains193
6 Mixed modules203
27 Uniqueness and refinements of decompositions in additive cate-gories204
28 Isotype,nice,and balanced submodules215
29 Categories Walk and Warf227
30 Simply presented modules236
31 Decomposition bases and extension of homomorphisms245
32 Warfield modules256
7 Determinity of modules by their endomorphism rings272
33 Theorems of Kaplansky and Wolfson273
34 Theorems of a topological isomorphism283
35 Modules over completions292
36 Endomorphisms of Warfield modules298
8 Modules with many endomorphisms or automorphisms308
37 Transitive and fully transitive modules308
38 Transitivity over torsion and transitivity mod torsion317
39 Equivalence of transitivity and full transitivity322
References333
Symbols351
Index353