Abstract
Characterizations of rings whose simple right R-modules are FGP-injective are investigated. It is proved that if R is a ring whose simple singular right R-modules are FGP-injective, then the center Z(R) of R is a von Neumann regular ring. As a corollary of this result we get if R is a ring whose simple singular right R-modules are GP-injective, then the center Z(R) of R is a von Neumann regular ring which is a generalization of the Nam's Proposition 3 in [3] which states "if R is a semiprime ring whose simple singular right R-modules are FGP-injective, then the center Z(R) of R is a von Neumann regular ring". It is also shown that if R satisfies l(a) subset of r(a), for any a is an element of R and every simple singular right R-modules are FGP-injective, then R is a reduced weakly regular ring.