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 $$u \in Z \left({R}\right) \Longrightarrow u^{-1} \in Z \left({R}\right)$$.

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