Module Theory, Extending Modules and Generalizations

  • Adnan Tercan
  • Canan C. Yücel

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Adnan Tercan, Canan C. Yücel
    Pages 1-74
  3. Adnan Tercan, Canan C. Yücel
    Pages 75-116
  4. Adnan Tercan, Canan C. Yücel
    Pages 117-174
  5. Adnan Tercan, Canan C. Yücel
    Pages 175-246
  6. Adnan Tercan, Canan C. Yücel
    Pages 247-319
  7. Adnan Tercan, Canan C. Yücel
    Pages 321-346
  8. Adnan Tercan, Canan C. Yücel
    Pages 347-348
  9. Back Matter
    Pages 349-369

About this book

Introduction

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.

Keywords

C11-module CS-module Goldie extending ring injective module triangular matrix ring

Authors and affiliations

  • Adnan Tercan
    • 1
  • Canan C. Yücel
    • 2
  1. 1.Fac. ScienceHacettepe UniversityAnkaraTurkey
  2. 2.Department of MathematicsPamukkale UniversityDenizliTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0952-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0950-4
  • Online ISBN 978-3-0348-0952-8
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • About this book