Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Module Theory, Extending Modules and Generalizations

  • Book
  • © 2016

Overview

Authors:
  1. Adnan Tercan

    1. Fac. Science, Hacettepe University, Ankara, Turkey

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Canan C. Yücel

    1. Department of Mathematics, Pamukkale University, Denizli, Turkey

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Frontiers in Mathematics (FM)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Introducing Modules

    • Adnan Tercan, Canan C. Yücel
    Pages 1-74

  3. Types of Relative Injectivity

    • Adnan Tercan, Canan C. Yücel
    Pages 75-116

  4. Extending Property and Related Concepts

    • Adnan Tercan, Canan C. Yücel
    Pages 117-174

  5. Inner Generalizations of Extending Modules

    • Adnan Tercan, Canan C. Yücel
    Pages 175-246

  6. Outer Generalizations of Extending Modules

    • Adnan Tercan, Canan C. Yücel
    Pages 247-319

  7. Dual Goldie and EC-complement Versions of the Extending Property

    • Adnan Tercan, Canan C. Yücel
    Pages 321-346

  8. Open Problems and Questions

    • Adnan Tercan, Canan C. Yücel
    Pages 347-348

  9. Back Matter

    Pages 349-369
    Download chapter PDF
Back to top

Keywords

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

“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)

Authors and Affiliations

  • Fac. Science, Hacettepe University, Ankara, Turkey

    Adnan Tercan

  • Department of Mathematics, Pamukkale University, Denizli, Turkey

    Canan C. Yücel

Bibliographic Information

  • Book Title: Module Theory, Extending Modules and Generalizations

  • Authors: Adnan Tercan, Canan C. Yücel

  • Series Title: Frontiers in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-0952-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Softcover ISBN: 978-3-0348-0950-4Published: 15 June 2016

  • eBook ISBN: 978-3-0348-0952-8Published: 13 May 2016

  • Series ISSN: 1660-8046

  • Series E-ISSN: 1660-8054

  • Edition Number: 1

  • Number of Pages: XX, 369

  • Topics: Associative Rings and Algebras

Publish with us

Policies and ethics

Back to top

Search

Navigation