Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Artinian Modules over Group Rings

  • Book
  • © 2007

Overview

Authors:
  1. Leonid A. Kurdachenko

    1. Department of Algebra School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Javier Otal

    1. Departamento de Matemáticas, Universidad de Zaragoza, Zaragoza, Spain

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Igor Ya. Subbotin

    1. Department of Mathematics and Natural Sciences, National University, Los Angeles, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • First book focussing on artinian modules
  • While usually the investigation of a corresponding ring structure precedes the study of a module over this ring, the book implements module properties through the artinian condition
  • Includes supplementary material: sn.pub/extras

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
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 (17 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Modules with chain conditions

    Pages 1-11

  3. Ranks of groups

    Pages 13-23

  4. Some generalized nilpotent groups

    Pages 25-35

  5. Artinian modules and the socle

    Pages 37-44

  6. Reduction to subgroups of finite index

    Pages 45-52

  7. Modules over Dedekind domains

    Pages 53-62

  8. The Kovacs-Newman theorem

    Pages 63-80

  9. Hartley’s classes of modules

    Pages 81-91

  10. The injectivity of some simple modules

    Pages 93-110

  11. Direct decompositions in artinian modules

    Pages 111-130

  12. On the countability of artinian modules over FC-hypercentral groups

    Pages 131-152

  13. Artinian modules over periodic abelian groups

    Pages 153-160

  14. Nearly injective modules

    Pages 161-166

  15. Artinian modules over abelian groups of finite section rank

    Pages 167-177

  16. The injective envelopes of simple modules over group rings

    Pages 179-188

  17. Quasifinite modules

    Pages 189-210

  18. Some applications: splitting over the locally nilpotent residual

    Pages 211-225

  19. Back Matter

    Pages 227-247
    Download chapter PDF
Back to top

Keywords

Reviews

From the reviews:

“The theory of modules over group rings RG for infinite groups G over arbitrary rings R is a very extensive and complex field of research with a great number of scattered results. … Since many of the results appear for the first time in a book it can be recommended warmly to any expert in this field, but also for graduate students who are presented the beauty of the interplay of the theories of groups, rings and representations.” (G. Kowol, Monatshefte für Mathematik, Vol. 152 (4), December, 2007)

Authors and Affiliations

  • Department of Algebra School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine

    Leonid A. Kurdachenko

  • Departamento de Matemáticas, Universidad de Zaragoza, Zaragoza, Spain

    Javier Otal

  • Department of Mathematics and Natural Sciences, National University, Los Angeles, USA

    Igor Ya. Subbotin

Bibliographic Information

  • Book Title: Artinian Modules over Group Rings

  • Authors: Leonid A. Kurdachenko, Javier Otal, Igor Ya. Subbotin

  • Series Title: Frontiers in Mathematics

  • DOI: https://doi.org/10.1007/978-3-7643-7765-6

  • Publisher: Birkhäuser Basel

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

  • Copyright Information: Birkhäuser Basel 2007

  • Softcover ISBN: 978-3-7643-7764-9Published: 23 October 2006

  • eBook ISBN: 978-3-7643-7765-6Published: 22 December 2006

  • Series ISSN: 1660-8046

  • Series E-ISSN: 1660-8054

  • Edition Number: 1

  • Number of Pages: XII, 247

  • Topics: Algebra

Publish with us

Policies and ethics

Back to top

Search

Navigation