On N–Flat Rings

Abstract

Let I be a right ideal of R, then R / I is a right N-flat if and only if for each a  I, there exists b  I and a positive integer n such that a n ≠ 0 and a n = ba n . In this paper, we first give and develop various properties of right N-flat rings, by which, many of the known results are extended. Also, we study the relations between such rings and regular, biregular ring.

On Simple Singular N-Flat Modules

“…Therefore , R is a right weakly regular . ▄ According to [1], rings satisfying condition (*), and right GQ -injective whose every simple singular right R-module is N-flat are always regular .But ,in general rings satisfying condition (*) and left GQ -injective whose every simple singular right Rmodule is N-flat need not be regular .This leads to the following theorem:…”

“…[ 7] , [8], [3] ). The generalization of flat module to N-flat module is performed as follows : Let I be a right ideal of a ring R, then R/I is a 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 = [1] . And , in [1] , we give a lot of characterizations of right N -flat .…”

On SNF-rings , I

“…is also monomorphism [1] . Generalizations on right flat modules have been studied by many authors (see [9] and [3]) . In [5] SF rings are defined and studied .…”