map of graded rings and projective schemes

Question

Let $\phi$ a morphism between $S$ and $R$, two graded rings (there is a $d>0$ such that $S_{n}$ maps to $R_{dn}$ for all $n$). How could I show that this induces a morphism of schemes $$\operatorname{Proj} R - V(\phi(S^+))\to \operatorname{Proj} S,$$ where $S^+$ is the irrelevant ideal?

Answer 1

As Cantlog says, this can be found in every introduction to algebraic geometry. For example EGA II, 2.8. Or Görtz-Wedhorn, Remark 13.7.