Kim, Jin Yong; Kim, Nam Kyun On rings containing a p-injective maximal left ideal. (English) Zbl 1101.16302 Commun. Korean Math. Soc. 18, No. 4, 629-633 (2003). Summary: We investigate 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. Cited in 1 Document MSC: 16D50 Injective modules, self-injective associative rings 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16D25 Ideals in associative algebras Keywords:von Neumann regular rings; p-injective ideals; p.p.-rings; finitely generated maximal left ideals PDF BibTeX XML Cite \textit{J. Y. Kim} and \textit{N. K. Kim}, Commun. Korean Math. Soc. 18, No. 4, 629--633 (2003; Zbl 1101.16302) Full Text: DOI OpenURL