# help me solve a problem

(a) Prove that, if I is a two-sided ideal of R, then the canonical homomorphism Z(R) $\rightarrow$ Z(R/I) is surjective.
(b) Let M be a left R-module and let S = $End_R(M)$. Prove that the homomorphism T : Z(R) $\rightarrow$ Z(S)
mT{r) = rm for r $\in$ R, m $\in$ M