Given Ring $\displaystyle R$ and $\displaystyle S\subseteq R$. If $\displaystyle C(S)=\{x\in R | xa=ax, \forall a \in S\}$ then show that $\displaystyle C(S)$ is the subring of $\displaystyle R$.
Given Ring $\displaystyle R$ and $\displaystyle S\subseteq R$. If $\displaystyle C(S)=\{x\in R | xa=ax, \forall a \in S\}$ then show that $\displaystyle C(S)$ is the subring of $\displaystyle R$.