Definition:Centralizer/Ring Subset

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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 $S$.

Linguistic Note

The UK English spelling of centralizer is centraliser.