Some Results on AWN-injective Rings

Abstract

A concept of AWN-injective ring is defined by [1], that is, for any   there exists  and an Y-sub module  of  (  is aright -module) such that  and  as left S-module with S=End(u ). If  is AWN-injective module, then we call  aright AWN-injective ring. In this note also continue to study some extensions of AWN-injective rings. A mong others it is proved that, if  is aright AWN-injective ring, so is for  satisfying . Also prove that  is reduced, and GW -reguler ring, if  is a weak symmetric and whose every simple right  -module is AWN-injective ring.