next up previous
Next: About this document ...

SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 885-889, October 2007




A NOTE ON PRINCIPALLY QUASI-INJECTIVE MODULES


BY


ZHANMIN ZHU




Abstract. Let $ R$ be a ring. In this note we study some properties of principally quasi-injective strongly Kasch $ R$-modules and show that if $ M_R$ is a principally quasi-injective strongly Kasch module, then $ R$ is semilocal if and only if $ _SM$ is finite dimensional, where $ S=end(M_R)$. This generalizes a result on rings obtained by Weimin Xue.

-------------------------

Received December 8, 2006; revised April 16, 2007.

AMS Subject Classification. 16D50, 16D70, 16L30.

Key words. principally quasi-injective modules, strongly Kasch modules.