On Rings whose Simple Singular R-Modules are GP-Injective

In this work we give a characterization of rings whose simple singular right R-modules are Gp-injective. We prove that if R is a quasi-duo ring whose simple singular right R-modules are Gp-injective, then any reduced right ideal of R is a direct summand. We also consider that a zero commutative ring with every simple singular left R-module is Gp-injective