《離散賦值環上的模》是2017年世界圖書出版公司出版的著作，作者是P.A.克雷洛夫（俄羅斯）、A.A.，圖根巴夫 。
基本介紹
- 中文名：離散賦值環上的模
- 作者：P.A.克雷洛夫（俄羅斯）、A.A.，圖根巴夫
- 出版社： 世界圖書出版公司
- 出版時間：2017年01月01日
- 開本：16 開
- 裝幀：平裝
- ISBN：9787519214760
內容簡介,目錄,
內容簡介
《離散賦值環上的模》向讀者呈現了離散賦值環上的模理論的概念、方法和定理，指出了離散賦值環和Abelian群之間的密切關係 ，書中有許多習題和一些有趣的開放性問題。這對代數專業的本科生、研究生和年輕的數學工作者很有參考意義。
目錄
Introduction
Preliminaries
1 Some definitions and notation
2 Endomorphisms and homomorphisms of modules
3 Discrete valuation domains
4 Primary notions of module theory
2 Basic facts
5 Free modules
6 Divisible modules
7 Pure submodules
8 Direct sums of cyclic modules
9 Basic submodules
10 Pure-projective and pure-injective modules
11 Complete modules
3 Endomorphism rings of divisible and complete modules
12 Examples of endomorphism tings
13 Harrison-Matlis equivalence
14 Jacobson radical
15 Galois correspondences
4 Representation of rings by eudomorphism rings
16 Finite topology
17 Ideal of finite endomorphisms
18 Characterization theorems for endomorphism rings of torsion-free modules
19 Realization theorems for endomorphism rings of torsion-free modules
20 Essentially indecomposable modules
21 Cotorsion modules and cotorsion hulls
22 Embedding of category of torsion-free modules in category of mixed modules
5 Torsion-free modules
23 Elementary properties of torsion-free modules
24 Category of quasihomomorphisms
25 Purely indecomposable and copurely indecomposable modules
26 Indecomposable modules over Nagata valuation domains
6 Mixed modules
27 Uniqueness and refinements of decompositions in additive cate-gories
28 Isotype, nice, and balanced submodules
29 Categories Walk and Warf
30 Simply presented modules
31 Decomposition bases and extension of homomorphisms
32 Warfield modules
7 Determinity of modules by their endomorphism rings
33 Theorems of Kaplansky and Wolfson
34 Theorems of a topological isomorphism
35 Modules over completions
36 Endomorphisms of Warfield modules
8 Modules with many endomorphisms or automorphisms
37 Transitive and fully transitive modules
38 Transitivity over torsion and transitivity mod torsion
39 Equivalence of transitivity and full transitivity
References
Symbols
Index
