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A RESULT ON SEMI-ARTINIAN RINGS

Published online by Cambridge University Press:  27 January 2003

Hai Quang Dinh
Affiliation:
Department of Mathematics, Ohio University, Athens, OH 45701, USA ([email protected])
Patrick F. Smith
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK ([email protected])
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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 $R$-moduleis injective. However, a characterization of rings, over which every finitely generated continuous rightmodule is injective, has been left open. In this note we give a partial solution for this question. Namely, we showthat for a right semi-artinian ring $R$, every finitely generated continuous right $R$-module is injective if and onlyif all simple right $R$-modules are injective.

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

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2003