Direct sum decompositions of infinitely generated modules
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- by D. J. Benson and Wayne W. Wheeler PDF
- Trans. Amer. Math. Soc. 351 (1999), 3843-3855 Request permission
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
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Additional Information
- D. J. Benson
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 34795
- 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
- Received by editor(s): November 12, 1997
- Published electronically: May 21, 1999
- Additional Notes: Both authors are partially supported by the NSF
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 3843-3855
- MSC (1991): Primary 20C20
- DOI: https://doi.org/10.1090/S0002-9947-99-02316-8
- MathSciNet review: 1608277