On Almost Weakly np – injective Rings

The ring R is called right almost weakly np injective, if for any , there exists a positive integer n and a left ideal of R such that . In this paper, we give some characterization and properties of almost weakly np injective rings. And we study the regularity of right almost weakly np injective ring and in the same time, when every simple (simple singular) right R module is almost weakly np injective, we also give some properties of an R.