Define a graded injective module over a graded ring $R$ to be an injective object in $GrMod-R$ (the category of right graded $R$-modules). From the little research I have done, a graded injective module is not necessarily injective. However, if it is graded and injective then it is graded injective.
Question Under what conditions on $R$, the graded injective modules are exactly the modules that are graded and injective?
I know that the latter always holds for graded projectives. Probably my question holds for Artin rings, or perhaps fd algebras (?), but I can't find a reference in the literature ,nor I can prove it...
