On weakly regular rings and SSF-rings

الملخص EN

In this work we consider weakly regular rings whose simple singular right R-Modules are flat.

We also consider the condition (*) : R satisfies L (a) Ír (a) for any aÎR.

We prove that if R satisfies (*) and whose simple singular right R-module are flat, then Z (R) the center of R is a von Neunann regular ring.

We also show that a ring R either satisfies (*) or a strongly right bounded ring in which every simple singular right R-module is flat, then R is reduced weakly regular rings.