Baer's Criterion for injectiveness of modules says: "An $R$-module $E$ is injective iff for all ideals $I$ of $R$, every homomorphism $f\colon I \to E$ can be extended to $R$." I wonder if there is a graded version for this? I mean:
Let $R$ be a graded ring. Let $M$ be a graded $R$-module.
If $Ext_R^1(R/I,E)=0$ for all homogeneous ideals $I$ of $R$ then $Ext_R^1(M,E)=0$ for every graded $R$-module $M$?