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Classes of modules with many direct summands

Part of: Modules, bimodules and ideals Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  09 April 2009

I. Al-Khazzi  and
P. F. Smith
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 K ⊆ N and N/K has Krull dimension at most α.

MSC classification

Secondary: 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation 16D60: Simple and semisimple modules, primitive rings and ideals 16P70: Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence 16P20: Artinian rings and modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 1 , August 1995 , pp. 8 - 19
Copyright
Copyright © Australian Mathematical Society 1995

References

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