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Decompositions of modules into projective modules and CS-modules

Published online by Cambridge University Press:  17 April 2009

Somyot Plubtieng
Somyot Plubtieng
Affiliation:
Department of Mathematics, Naresuan University, Phitsanulok 65000, Thailand e-mail: somyotp@nu.ac.th
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Abstract

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Let M be a right R-module. It is shown that M is a locally Noetherian module if every finitely generated module in σ[M] is a direct sum of a projective module and a CS-module. Moreover, if every module in σ[M] is a direct sum of a projective module and a CS-module, then every module in σ[M] is a direct sum of modules which are either indecomposable projective or uniform Σ-quasi-injective. In particular, if every module in σ[M] is a direct sum of a projective module and a quasi-continuous module, then every module in σ[M] is a direct sum of a projective module and a quasi-injective module.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 159 - 164
Copyright
Copyright © Australian Mathematical Society 2000

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