Module Theory, Extending Modules and Generalizations
Published on 15. June 2016
Book
Paperback/Softback
XX, 369 pages
978-3-0348-0950-4 (ISBN)
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.
Reviews / Votes
"Notably, each chapter ends with a (shorter or longer) list of exercises complementing the material of the book as well as with some useful historical and bibliographical remarks. . The book is well written, and takes readers thoroughly into the theory of extending modules and their generalizations. I consider this volume a valuable tool and source of inspiration both for students interested in future research in an active field of algebra and for working researchers." (Septimiu Crivei, Mathematical Reviews, May, 2017)"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)
More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XX, 369 p.
Dimensions
Height: 240 mm
Width: 168 mm
Thickness: 22 mm
Weight
656 gr
ISBN-13
978-3-0348-0950-4 (9783034809504)
DOI
10.1007/978-3-0348-0952-8
Schweitzer Classification
Other editions
Additional editions
Adnan Tercan | Canan C. Yücel
Module Theory, Extending Modules and Generalizations
E-Book
05/2016
Birkhäuser
€106.99
Available for download
Content
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.