Themes in Torsion Theory

The purpose of this book is to generalize to the§torsion-theoretic setting various concepts and§results from the theory of rings and modules. In§particular we work in the areas of chain conditions§on modules, injectivity and CS (extending) modules.§§At the outset we acquaint the reader with the main§ideas used in torsion theory. We then obtain results§that fall into three more or less interrelated areas.§In the first area we introduce a torsion-theoretic§analogue of Max modules and generalize an important§characterization of Noetherian rings by Shock. The§second area deals with various flavors of relative§injectivity. We generalize well-known results by§Fuchs, Azumaya, Faith, Albu and Nastasescu and§Cailleau. In the third area we introduce a couple of§new concepts with the aim of bringing to the§torsion-theoretic setting the concept of a CS or§extending module. Our motivation is to provide a§torsion-theoretic analogue of a celebrated result by§Okado.§§This book should appeal to researchers in the theory§of rings and modules with particular emphasis on§torsion theory.