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Module theory, extending modules and generalizations / by Adnan Tercan, Canan C. Yücel.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Tercan, Adnan., Author.
- Yücel, Canan C., Author.
- Series:
- Frontiers in Mathematics, 1660-8046
- Language:
- English
- Subjects (All):
- Associative rings.
- Rings (Algebra).
- Associative Rings and Algebras.
- Local Subjects:
- Associative Rings and Algebras.
- Physical Description:
- 1 online resource (389 p.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Basel : Springer Basel : Imprint: Birkhäuser, 2016.
- Summary:
- 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.
- 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.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references and index.
- ISBN:
- 3-0348-0952-2
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