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Trends in Mathematics

Infinite Length Modules

Editors: Krause, Henning, Ringel, Claus M. (Eds.)

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About this book

This volume presents the invited lectures of a conference devoted to Infinite Length Modules, held at Bielefeld, September 7-11, 1998. Some additional surveys have been included in order to establish a unified picture. The scientific organization of the conference was in the hands of K. Brown (Glasgow), P. M. Cohn (London), I. Reiten (Trondheim) and C. M. Ringel (Bielefeld). The conference was concerned with the role played by modules of infinite length when dealing with problems in the representation theory of algebras. The investi­ gation of such modules always relies on information concerning modules of finite length, for example simple modules and their possible extensions. But the converse is also true: recent developments in representation theory indicate that a full un­ derstanding of the category of finite dimensional modules, even over a finite dimen­ sional algebra, requires consideration of infinite dimensional, thus infinite length, modules. For instance, the important notion of tameness uses one-parameter fami­ lies of modules, or, alternatively, generic modules and they are of infinite length. If one tries to exhibit a presentation of a module category, it turns out to be essential to take into account the indecomposable modules which are algebraically compact, or, equivalently, pure injective. Specific methods have been developed over the last few years dealing with such special situations as group algebras of finite groups or noetherian rings, and there are surprising relations to topology and geometry. The conference outlined the present state of the art.

Table of contents (23 chapters)

  • Infinite Length Modules. Some Examples as Introduction

    Ringel, Claus Michael

    Pages 1-73

  • Modules with Strange Decomposition Properties

    Eklof, Paul C.

    Pages 75-87

  • Failure of the Krull-Schmidt Theorem for Artinian Modules and Serial Modules

    Facchini, Alberto

    Pages 89-99

  • Artinian Modules Over a Matrix Ring

    Pimenov, K. I. (et al.)

    Pages 101-105

  • Some Combinatorial Principles for Solving Algebraic Problems

    Göbel, Rüdiger

    Pages 107-127

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-0348-8426-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-0348-9562-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Infinite Length Modules
Editors
  • Henning Krause
  • Claus M. Ringel
Series Title
Trends in Mathematics
Copyright
2000
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8426-6
DOI
10.1007/978-3-0348-8426-6
Softcover ISBN
978-3-0348-9562-0
Series ISSN
2297-0215
Edition Number
1
Number of Pages
IX, 439
Topics