Some comments on simple singular GP-injective modules (Q2755635)

Let \(R\) be an associative ring with nonzero identity element. A right \(R\)-module \(M\) is said to be generalized principally injective, for short GP-injective, if for any nonzero element \(r\in R\) there exists a positive integer \(n\) such that \(r^n\neq 0\) and any \(R\)-linear map from \(r^nR\) into \(M\) extends to one from \(R\) into \(M\). The authors investigate von Neumann type regularity conditions on rings \(R\) whose simple singular right \(R\)-modules are GP-injective.