\begin{definition}[Definition:Centralizer/Ring Subset]
Let $S$ be a subset of a ring $\struct {R, +, \circ}$.
The '''centralizer of $S$ in $R$''' is defined as:
:$\map {C_R} S = \set {x \in R: \forall s \in S: s \circ x = x \circ s}$
That is, the '''centralizer of $S$''' is the set of elements of $R$ which commute with all elements of $S$.
\end{definition}