J Austral Math Soc Ser A 59 pp8--19, 1995.

Classes of Modules with many Direct Summands

I. Al-Khazzi and P. F. Smith

Abstract

Let R be any ring with identity, M a unital right R-module and a ³ 0 an ordinal. Then M is a direct sum of a semisimple module and a module having Krull dimension at most a if and oonly if for every submodule N of M there exists a direct summand K of M such that K Í N and N/K has Krull dimension at most a.

1991 AMS Subject Classification: primary 16D70; secondary 16D60, 16P70, 16P20

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Authors

I. Al-Khazzi

P. F. Smith

Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK.