Definition:Centralizer/Ring Subset

Definition
Let $S$ be a subset of a ring $\left({R, +, \circ}\right)$.

The centralizer of $S$ in $R$ is defined as:


 * $C_R \left({S}\right) = \left\{{x \in R: \forall s \in S: s \circ x = x \circ s}\right\}$

That is, the centralizer of $S$ is the set of elements of $R$ which commute with all elements of $S$.

Linguistic Note
The UK English spelling of this is centraliser.