Center of Ring is Commutative Subring

Theorem
The center $Z \left({R}\right)$ of a ring $R$ is a commutative subring of $R$.

If $u \in U_R$, then $u \in Z \left({R}\right) \implies u^{-1} \in Z \left({R}\right)$.

Proof
Follows directly from the definition of center and Centralizer of Ring Subset is Subring.