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ON RINGS CONTAINING A P-INJECTIVE MAXIMAL LEFT IDEAL

Kim, Jin-Yong;Kim, Nam-Kyun

  • Published : 2003.10.01

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

References

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Cited by

  1. Left Rings vol.2011, 2011, https://doi.org/10.1155/2011/294301
  2. On Rings Containing a Non-essential nil-Injective Maximal Left Ideal vol.52, pp.2, 2012, https://doi.org/10.5666/KMJ.2012.52.2.179