Abstract
AbstractIt 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
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