Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Direct sum decompositions
of infinitely generated modules


Authors: D. J. Benson and Wayne W. Wheeler
Journal: Trans. Amer. Math. Soc. 351 (1999), 3843-3855
MSC (1991): Primary 20C20
Published electronically: May 21, 1999
MathSciNet review: 1608277
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Almost all of the basic theorems in the representation theory of finite groups have proofs that depend upon the Krull-Schmidt Theorem. Because this theorem holds only for finite-dimensional modules, however, the recent interest in infinitely generated modules raises the question of which results may hold more generally. In this paper we present an example showing that Green's Indecomposability Theorem fails for infinitely generated modules. By developing and applying some general properties of idempotent modules, we are also able to construct explicit examples of modules for which the cancellation property fails.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20C20

Retrieve articles in all journals with MSC (1991): 20C20


Additional Information

D. J. Benson
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: djb@byrd.math.uga.edu

Wayne W. Wheeler
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Address at time of publication: Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, England
Email: www@sloth.math.uga.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02316-8
PII: S 0002-9947(99)02316-8
Received by editor(s): November 12, 1997
Published electronically: May 21, 1999
Additional Notes: Both authors are partially supported by the NSF
Article copyright: © Copyright 1999 American Mathematical Society