Let $X = \operatorname{Proj}( R[X,Y,Z]/(j))$ ( $j$ is a homogenous polynomial). Assume that $\Gamma(X, \mathcal{O}_{X }) = R$ form simplicity.
Suppose that there is a map of graded $R$-algebra $f:R[X,Y,Z]/(j) \to R[X,Y,Z]/(j)$ such that it induces a morphism of schemes $f:X \to X$ . Since $f$ is a morphism of scheme this means there should be an induced map from $\Gamma(X, \mathcal{O}_{X }) \to \Gamma(X, \mathcal{O}_{X })$, i.e a map from $R \to R$.
How does one find out what is this induced map?
I think it will be identity because it is an $R$-algebra homomorphism.
(Edited the previous version of the question)