Lifting Modules Supplements and Projectivity in Module Theory
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and te
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Contents Preface
vii
Introduction
ix
Notation
xiii
1 Basic notions 1 Preliminaries . . . . . . . . . . . . . . . . . 2 Small submodules and the radical . . . . . . 3 Cosmall inclusions and coclosed submodules 4 Projectivity conditions . . . . . . . . . . . . 5 Hollow dimension of modules . . . . . . . . 2 Preradicals and torsion theories 6 Preradicals and colocalisation . . . . . . . 7 Torsion theories . . . . . . . . . . . . . . . 8 Torsion theories related to small modules 9 Corational modules . . . . . . . . . . . . . 10 Proper
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