Let $R$ be a ring. A $R$-module is an abelian group $M$ with an application $R\times M\longrightarrow M$, $(r, x)\longmapsto r\cdot x$ satisfying some properties.
To give a $R$-module structure on an abelian group is equivalent to give a ring homomorphism $R\longrightarrow \mathsf{End}(M)$. Does this generalizes to graded modules? More precisely, given a graded ring $R$, can one see a graded $R$-module structure on a graded abelian group $M$ as a graded endomorphism from $R$ to something? How about graded modules over graded algebras?
Thanks.