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

Abstract
A ring R is called left AGP-injective if for any 0 ≠ a R, there exists a positive integer
n such that a
n ≠ 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 {X
an: 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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