Some Comments on Simple Singular GP-Injective Modules

We investigate in this paper von Neumann regularity of rings whose simple singular right R-modules are GP-injective. 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 GP-injective. And it is also shown that if R is a PI-ring whose simple singular right R-modules are GP-injective, then R is a strongly π-regular ring. Finally, it is proved that if R is a right continuous ring whose simple singular right R-modules are GP- injective, then R is von Neumann regular.