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Some remarks on CS modules and SI rings

Published online by Cambridge University Press:  17 April 2009

Dinh Van Huynh
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
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 461 - 466
Copyright
Copyright © Australian Mathematical Society 2002

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