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

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-Erbil, Kurdistan Region Iraq

E-mail:abdullah.abduljabbar@su.edu.krd


Article info

Original: 27 Mar 2015
Revised: 1 May 2015
Accepted: 31 May 2015
Published online:  
20 Dec. 2015
           

Key Words: 
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 Î 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 AGP-injective. 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 Î R and n is a positive integer} of ideals such that Xanb  = Xban, for all a, b Î R and a positive integer n.    


Ċ
Kewan Omer,
Dec 22, 2015, 1:39 PM