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Module Theory, Extending Modules and Generalizations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Module Theory, Extending Modules and Generalizations/ by Adnan Tercan, Canan C. Yücel.
Author:	Tercan, Adnan.
other author:	Yücel, Canan C.
Description:	XX, 369 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Associative rings. -
Online resource:	https://doi.org/10.1007/978-3-0348-0952-8
ISBN:	9783034809528

Module Theory, Extending Modules and Generalizations
Tercan, Adnan.

Module Theory, Extending Modules and Generalizations[electronic resource] /by Adnan Tercan, Canan C. Yücel. - 1st ed. 2016. - XX, 369 p.online resource. - Frontiers in Mathematics,1660-8046. - Frontiers in Mathematics,.

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.

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.

ISBN: 9783034809528

Standard No.: 10.1007/978-3-0348-0952-8doiSubjects--Topical Terms:

893564
Associative rings.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Module Theory, Extending Modules and Generalizations
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520 $a 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.
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