الملخص

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.