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醉染图书离散赋值环上的模9787519214760
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Introduction
1 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 Comle&bsp;modules
3 Endomorphism rings of divisible and comle&bsp;modules
12 Examples of endomorphism rings
13 Harrison—Matlis equivalence
14 Jacobson radical
15 Galois correspondences
4 Representation of rings by endomorphism rings
16 Finite topology
17 Ideal of finite endomorphisms
18 Characterization theorems for endomorphism rings of torsionfree modules
19 Realization theorems for endomorphism rings of torsion—free modules
20 Essentially indecoable modules
21 Cotorsion modules and cotorsion hulls
22 Embedding of category of torsion—free modules in category of mixed modules
5 Torsion—free modules
Elementary properties of torsion—free modules
24 Category of quasihomomorphisms
25 Purely indecoable and copurely indecoable modules
26 Indecoable modules over Nagata valuation domains
6 Mixed modules
27 Uniqueness and refinements of decoitions in additive categories
28 Isotype, nice, and balanced submodules
29 Categories Walk and Warf
30 Simply presented modules
31 Decoition 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 comlios
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
(俄罗斯)P.A.雷洛夫(Piotr A.Krylov),(俄罗斯)A.A.图根巴夫(Askar A.Tuganbaev),是俄罗斯有名数学家,本书是为代数专业撰写的教材。
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