Module Theory, Extending Modules and Generalizations

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.

Provides a comprehensive introduction to module theory with clear explanations Complements results on CS-modules and CS-rings from former monographs addressing this trend Presents cutting-edge research on generalizations of CS-modules and CS-rings Features a wealth of examples and open problems

Inhalt
Preface.- Introduction.- List of Symbols.- Introducing modules.- Types of Relative Injectivity.- Extending Property and Related Concepts.- Inner Generalizations of Extending Modules.- Outer Generalizations of Extending Modules.- Dual Goldie and EC-complement Versions of the Extending Property.- Open Problems and Questions.- Appendix.- References.- Index.