离散赋值环上的模PDF电子书下载

1 Preliminaries 1

1 Some definitions and notation 1

2 Endomorphisms and homomorphisms of modules 7

3 Discrete valuation domains 16

4 Primary notions of module theory 31

2 Basic facts 46

5 Free modules 46

6 Divisible modules 49

7 Pure submodules 55

8 Direct sums of cyclic modules 60

9 Basic submodules 65

10 Pure-projective and pure-injective modules 72

11 Complete modules 77

3 Endomorphism rings of divisible and complete modules 86

12 Examples of endomorphism rings 87

13 Harrison-Matlis equivalence 89

14 Jacobson radical 94

15 Galois correspondences 105

4 Representation of rings by endomorphism rings 116

16 Finite topology 117

17 Ideal of finite endomorphisms 119

18 Characterization theorems for endomorphism rings of torsion-free modules 126

19 Realization theorems for endomorphism rings of torsion-free modules 134

20 Essentially indecomposable modules 141

21 Cotorsion modules and cotorsion hulls 146

22 Embedding of category of torsion-free modules in category of mixed modules 156

5 Torsion-free modules 166

23 Elementary properties of torsion-free modules 167

24 Category of quasihomomorphisms 170

25 Purely indecomposable and copurely indecomposable modules 180

26 Indecomposable modules over Nagata valuation domains 193

6 Mixed modules 203

27 Uniqueness and refinements of decompositions in additive cate-gories 204

28 Isotype,nice,and balanced submodules 215

29 Categories Walk and Warf 227

30 Simply presented modules 236

31 Decomposition bases and extension of homomorphisms 245

32 Warfield modules 256

7 Determinity of modules by their endomorphism rings 272

33 Theorems of Kaplansky and Wolfson 273

34 Theorems of a topological isomorphism 283

35 Modules over completions 292

36 Endomorphisms of Warfield modules 298

8 Modules with many endomorphisms or automorphisms 308

37 Transitive and fully transitive modules 308

38 Transitivity over torsion and transitivity mod torsion 317

39 Equivalence of transitivity and full transitivity 322

References 333

Symbols 351

Index 353