\begin{definition}[Definition:Center (Abstract Algebra)/Ring]
The '''center of a ring''' $\struct {R, +, \circ}$, denoted $\map Z R$, is the subset of elements in $R$ that commute under $\circ$ with every element in $R$.
Symbolically:
:$\map Z R = \map {C_R} R = \set {x \in R: \forall s \in R: s \circ x = x \circ s}$
{{ExtractTheorem}}
That is, the '''center of $R$''' is the centralizer of $R$ in $R$ itself.
It is clear that the '''center of a ring''' $\struct {R, +, \circ}$ can be defined as the center of the semigroup $\struct {R, \circ}$.
\end{definition}