On Almost J - injectivity and J –Regularity of Rings

Abstract

As a generalization of right J- injective rings , we introduce the notion of right almost J-injective rings , that is if for any , there exists a left ideal of R such that . In this paper , we give some characterizations and properties of almost J-injective rings and it is show that R is J-regular if and only if R is a right almost J-injective and JPP ring . We also prove that , if R is right quasi duo , then R is J-regular if and only if every simple right R-module is almost J-injective .