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The endomorphism ring of a finite-length module

Published online by Cambridge University Press:  17 April 2009

Rainer Schulz
Rainer Schulz
Affiliation:
Department of Algebra, Combinatorics and Analysis, Auburn University, Alabama 36849, United States of America
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Abstract

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Let M be an R-module of finite length. For a simple R-module A, let ℓA denote the nuber of times the isomorphism type of A appears in a composition chain of M, and let σ denote the maxinium of the ℓA, A ranging over all simple submodules of M. Let S be the endomorphism ring of M. We show that the Loewy length of S is bounded by σ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 141 - 143
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Bourbaki, N., Algèbre: Modules et Anneaux semi-simples, Chap. 8 (Hermann, Paris, 1958).Google Scholar
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[4]Smalø, S.O., ‘A limit on the Loewy length of the endomorphism ring of a module of finite length’, Proc. Amer. Math. Soc. 81 (1981), 164–166.CrossRefGoogle Scholar