Module Theory, Extending Modules and Generalizations

Description

The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises. Front Matter....Pages i-xx Introducing Modules....Pages 1-74 Types of Relative Injectivity....Pages 75-116 Extending Property and Related Concepts....Pages 117-174 Inner Generalizations of Extending Modules....Pages 175-246 Outer Generalizations of Extending Modules....Pages 247-319 Dual Goldie and EC-complement Versions of the Extending Property....Pages 321-346 Open Problems and Questions....Pages 347-348 Back Matter....Pages 349-369