离散赋值环上的模(英文版)

P.A.克雷洛夫、A.A.图根巴夫著的《离散赋值环 上的模》向读者呈现了离散赋值环上的模理论的概念 、方法和定理，指出了离散赋值环和Abelian群之间 的密切关系 ，书中有许多习题和一些有趣的开放性 问题。这对代数专业的本科生、研究生和年轻的数学 工作者很有参考意义。

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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