Definition:Centralizer/Ring Subset

From ProofWiki
Jump to navigation Jump to search

Definition

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.


Sources