On n-flat modules and n-Von Neumann regular rings

Abstract

We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n−1)-ring (resp., a weakly (n,n−1)-ring). We also give a new characterization of n-Von Neumann regular rings and a characterization of weak n-Von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-Von Neumann regular ring is a (CH)-ring.