Description
Birkhauser Module Theory Extending Modules and Generalizations by Adnan Tercan, Canan C. Yucel
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._x000D__x000D_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._x000D__x000D_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._x000D_ Table of contents :- _x000D_
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._x000D_