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On rings containing a p-injective maximal left ideal. (English) Zbl 1101.16302

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.

MSC:

16D50 Injective modules, self-injective associative rings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16D25 Ideals in associative algebras
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