[[Ring theory MOC]]
# Centre of a rng

The **centre** $\mathrm{Z}(R)$ of a [[rng]] $R$ is the [[subrng]] consisting of all elements of $R$ that commute with every other element, i.e. $\mathrm{Z}(R) = \{ a \in R \mid ax=xa \quad \forall x \in R \}$. #m/def/ring
This is entirely analogous with the [[centre of a group]].

## Properties

- The centre is necessarily a [[commutative ring]]
- If $R$ is a [[ring]] then $1 \in Z(R)$

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#state/tidy | #lang/en | #SemBr