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