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

Authors

  • Abdullah M. Abdul-Jabbar Department of Mathematics, College of Science, Salahaddin University, Erbil, Kurdistan Region, Iraq. Author

DOI:

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

Keywords:

AP-injective modules, AGP-injective modules, AGP-injective rings, Regular rings

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.

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Published

2015-05-31

How to Cite

On Simple Singular AGP-Injective Modules and AGP-Injective Rings with Some Types of Regular Rings. (2015). Journal of Zankoy Sulaimani - Part A, 17(4), 51-62. https://doi.org/10.17656/jzs.10424