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Frontiers in Mathematics

Module Theory, Extending Modules and Generalizations

Authors: Tercan, Adnan, Yücel, Canan C.

  • Provides a comprehensive introduction to module theory with clear explanations
  • Complements results on CS-modules and CS-rings from former monographs addressing this trend
  • Presents cutting-edge research on generalizations of CS-modules and CS-rings
  • Features a wealth of examples and open problems
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eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0952-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-0348-0950-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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

“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)


Table of contents (7 chapters)

  • Introducing Modules

    Tercan, Adnan (et al.)

    Pages 1-74

  • Types of Relative Injectivity

    Tercan, Adnan (et al.)

    Pages 75-116

  • Extending Property and Related Concepts

    Tercan, Adnan (et al.)

    Pages 117-174

  • Inner Generalizations of Extending Modules

    Tercan, Adnan (et al.)

    Pages 175-246

  • Outer Generalizations of Extending Modules

    Tercan, Adnan (et al.)

    Pages 247-319

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0952-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-0348-0950-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Module Theory, Extending Modules and Generalizations
Authors
Series Title
Frontiers in Mathematics
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-0348-0952-8
DOI
10.1007/978-3-0348-0952-8
Softcover ISBN
978-3-0348-0950-4
Series ISSN
1660-8046
Edition Number
1
Number of Pages
XX, 369
Topics