On Almost Weakly np – injective Rings

Abstract

The ring R is called right almost weakly np – injective, if for any a∈N_2 (R), there exists a positive integer n and a left ideal X_(a^n ) of R such that lr(a^n )=Ra^n⨁X_(a^n ). 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.