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

Abdullah M. Abdul-Jabbar

Department of Mathematics, College of Science, Salahaddin University

DOI: https://doi.org/10.17656/jzs.10424

Abstract

A ring R is called left AGP-injective if for any 0 ≠ a ∈ R, there exists a positive integer

n such that an ≠ 0 and anR is a direct summand of rℓ(an). Now, in the present paper, we

invistigate some properties of rings whose simple singular right R-modules are AGPinjective. Also, we give a characterization of π-regular rings interms of right weakly

continuous ring whose simple singular right R-modules are AGP-injective under the

condition, MERT ring. Finally, we give a property of AGP-injective rings with an

index set {Xan: a ∈ R and n is a positive integer} of ideals such that Xanb = Xban, for

all a, b ∈ R and a positive integer n. 

Key Words: AP-injective modules, AGP-injective modules, AGP-injective rings, regular rings. 

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