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 Complete modules 3 Endomorphism rings of divisible and complete 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 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 categories 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
