On Simple Singular AGP-Injective Modules and AGP-Injective Rings with Some Types of Regular Rings

Abstract

A ring R is called left AGP-injective if for any 0 ≠ a ∈ R, there exists a positive integern such that an ≠ 0 and anR is a direct summand of rℓ(an). Now, in the present paper, weinvistigate some properties of rings whose simple singular right R-modules are AGPinjective. Also, we give a characterization of π-regular rings interms of right weaklycontinuous ring whose simple singular right R-modules are AGP-injective under thecondition, MERT ring. Finally, we give a property of AGP-injective rings with anindex set {Xan: a ∈ R and n is a positive integer} of ideals such that Xanb = Xban, forall a, b ∈ R and a positive integer n.