On Rings Whose Simple Singular R-Modules Are Flat, I

In this paper we investigate von Neumann regularity of rings whose simple singular right R-modules are flat. It is proved that a ring R is strongly regular if and only if R is a semiprime right quasi-duo ring whose simple singular right R-modules are flat. Moreover, it is shown that if R is a P. I.-ring whose simple singular right R-modules are flat, then R is a strongly p-regular ring. Finally, it is shown that if R is a right continuous ring whose simple singular right R-modules are flat, then R is a von Neumann regular ring.