On Simple Singular N-Flat Modules

Abstract

Let I be a right ideal of a ring R , then R/I is right N-flat module if and only if for each I a , there exists I b and a positive integer n such that 0  n a and n n ba a = .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.