On rings whose simple singular R-modules are flat, I

الملخص EN

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 - 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.