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Rings Whose Simple Singular Modules are PS-Injective

Xiang, Yueming;Ouyang, Lunqun

  • Received : 2012.11.13
  • Accepted : 2013.04.20
  • Published : 2014.09.23

Abstract

Let R be a ring. A right R-module M is PS-injective if every R-homomorphism $f:aR{\rightarrow}M$ for every principally small right ideal aR can be extended to $R{\rightarrow}M$. We investigate, in this paper, rings whose simple singular modules are PS-injective. New characterizations of semiprimitive rings and semisimple Artinian rings are given.

Keywords

PS-injective modules;semiprimitive rings;nonsingular rings

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