On Simple Singular N-Flat Modules

Let I be a right ideal of a ring R , then R/I is right N-flat module if and only if for each , there exists and a positive integer n such that and .In this paper, we first introduce and characterize rings whose every simple singular right R-module is N - flat. Next, we investigate the strong regularity of rings whose every simple singular right R - module is N-flat. It is proved that :
R is strongly regular ring if and only if R is a wjc , MERT and 2 - primal ring whose simple singular right R- module is N - flat.
Let R be a wjc ring satisfying condition (*). If every simple singular right R-module is N-flat .Then, the Center of R is a regular ring.