On simple singular N-flat modules

Abstract EN

-Let I be a right ideal of a ring R , then R/I is right N-flat module if and only if for each aI , there exists bI and a positive integer n such that an  0 and an ban .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 Rmodule is N-flat .Then, the Center of R is a regular ring.