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

Volume 17 , Issue 4 , December 2015 , Pages 51-62

Authors

Abdullah M. Abdul-Jabbar 1

1 Department of Mathematics, College of Science, Salahaddin University

DOI logo 10.17656/jzs.10424

Keywords

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.

Statistics
  • Article view374
  • Downloads0
  • Published at20 December 2015

  • RIS
  • BibTeX
  • EndNote
  • Mendeley
  • APA (7th edition)
  • MLA (9th edition)
  • Chicago
  • Harvard
  • IEEE
  • Vancouver