Module Theory, Extending Modules and Generalizations by Adnan TercanModule Theory, Extending Modules and Generalizations by Adnan Tercan

Module Theory, Extending Modules and Generalizations

byAdnan Tercan, Canan C. Yücel

Paperback | June 15, 2016

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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.

Title:Module Theory, Extending Modules and GeneralizationsFormat:PaperbackDimensions:369 pagesPublished:June 15, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034809506

ISBN - 13:9783034809504


Table of Contents

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.

Editorial Reviews

"The book is addressed to students and researchers in module and ring theory. It will undoubtedly be a valuable tool for everybody working in this area. Finally, it should be mentioned that the authors have made a well-thought-out effort to improve and refine the terminology on the subject." (Bin Zhu, zbMATH 1368.16002, 2017)