Definition:Centralizer/Ring Subset
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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 $S$.
Also see
Linguistic Note
The UK English spelling of centralizer is centraliser.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $21$. Rings and Integral Domains