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Annihilators and the CS-condition

Published online by Cambridge University Press:  18 May 2009

W. K. Nicholson  and
M. F. Yousif
W. K. Nicholson
Affiliation:
Department of Mathematics, University of Calgary, Calgary, CanadaT2N 1N4
M. F. Yousif
Affiliation:
Department of Mathematics, Ohio State University, Lima, Ohio 45804, USA
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Abstract

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It is proved that if every cyclic right R-module is torsionless and R is a left CS-ring then R is semiperfect left continuous with soc(RR)essential in RR. As a consequence every right cogenerator, left CS-ring R is shown to be right pseudo-Frobenius and left continuous, and an example is given to show that R need not be left selfinjective. It is also proved that if R is a left CS-ring and every cyclic right R-module embeds in a free module, then R is quasi-Frobenius if and only if J(R) ⊆ Z(RR).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 213 - 222
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

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