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A RESULT ON SEMI-ARTINIAN RINGS

Published online by Cambridge University Press:  27 January 2003

Hai Quang Dinh  and
Patrick F. Smith
Hai Quang Dinh
Affiliation:
Department of Mathematics, Ohio University, Athens, OH 45701, USA (haidinh@email.msn.com)
Patrick F. Smith
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK (pfs@maths.gla.ac.uk)
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Abstract

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It was shown by Huynh and Rizvi that a ring $R$ is semisimple artinian if and only if every continuous right $R$-module is injective. However, a characterization of rings, over which every finitely generated continuous right module is injective, has been left open. In this note we give a partial solution for this question. Namely, we show that for a right semi-artinian ring $R$, every finitely generated continuous right $R$-module is injective if and only if all simple right $R$-modules are injective.

AMS 2000 Mathematics subject classification: Primary 16D50. Secondary 16P20; 16P60

Keywords

$V$ ringsemi-artinian ringCS moduleinjective module
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 1 , February 2003 , pp. 63 - 66
Copyright
Copyright © Edinburgh Mathematical Society 2003