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Some remarks on CS modules and SI rings

Published online by Cambridge University Press:  17 April 2009

Dinh Van Huynh
Affiliation:
Department of Mathematics, Ohio University, Athens OH 45701, United States of America, e-mail: huynh@math.ohiou.edu
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Abstract

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We discuss some results on CS modules, SI rings, and SC rings. Then we consider the question of when, over a right SC ring R, every right R-module is CS. In Theorem 3.1 we show that this is the case if and only if R is a right countably Σ-CS ring. In light of this, we give an example showing that a result proved by Chen (2000) is incorrect. Furthermore, Theorem 4.1 shows that the assumptions of Chen (2000) can be weakened considerably.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

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