On rings containing a p-injective maximal left ideal
Commun. Korean Math. Soc. 2003 Vol. 18, No. 4, 629-633
Printed December 1, 2003
Jin Yong Kim, Nam Kyun Kim
Kyung Hee University, Hanbat National University
Abstract : We investigate in this paper rings containing a finitely generated p-injective maximal left ideal. We show that if $R$ is a semiprime ring containing a finitely generated p-injective maximal left ideal, then $R$ is a left p-injective ring. Using this result we are able to give a new characterization of von Neumann regular rings with nonzero socle.
Keywords : von Neumann regular rings, p-injective ideals, p.p.-rings
MSC numbers : 16D50, 16E50
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