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Subdirect product of PS-rings need not be PS

Published online by Cambridge University Press:  17 April 2009

Weimin Xue
Weimin Xue
Affiliation:
Department of Mathematics, Fujian Normal University, Fuzhou, Fujian 350007 People's, Republic of China
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Abstract

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An associative ring R with identity is called a PS-ring if soc(RR) is projective. We construct a non- PS-ring R which is a subdirect product of two PS-rings, thus answering a question of Nicholson and Watters in the negative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 3 , December 1990 , pp. 525
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Nicholson, W.K. and Watters, J.F., ‘Rings with projective socle’, Proc. Amer. Math. Soc. 102 (1988), 443–450.CrossRefGoogle Scholar