Module Theory, Extending Modules and Generalizations / Frontiers in Mathematics (PDF)
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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.
- Autoren: Adnan Tercan , Canan C. Yücel
- 2016, 1st ed. 2016, 369 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3034809522
- ISBN-13: 9783034809528
- Erscheinungsdatum: 13.05.2016
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- Grösse: 4.10 MB
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“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)
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