On Simple Singular AGP-Injective Modules and AGP-Injective Rings with Some Types of Regular Rings - Abdul-Jabbar, Abdullah M. (Sulaimani Journal for Pure and Applied Sciences, 2015)
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.
Keywords: APinjective modules; AGPinjective modules; AGPinjective rings; regular rings