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Classes of modules with many direct summands

Published online by Cambridge University Press:  09 April 2009

I. Al-Khazzi
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK
P. F. Smith
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK
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Abstract

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Let R be any ring with identity, M a unital right R-module and α ≥ 0 an ordinal. Then M is a direct sum of a semisimple module and a module having Krull dimension at most α if and only if for every submodule N of M there exists a direct summand K of M such that KN and N/K has Krull dimension at most α.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

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