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In algebra, the **centre of a ring** *R* is the subring consisting of the elements *x* such that *xy* = *yx* for all elements *y* in *R*. It is a commutative ring and is denoted as Z(*R*); 'Z' stands for the German word *Zentrum*, meaning "centre".

If *R* is a ring, then *R* is an associative algebra over its centre. Conversely, if *R* is an associative algebra over a commutative subring *S*, then *S* is a subring of the center of *R*, and if *S* happens to be the center of *R*, then the algebra *R* is called a **central algebra**.

- The centre of a commutative ring
*R*is*R*itself. - The centre of a skew-field is a field.
- The centre of the (full) matrix ring with entries in a commutative ring
*R*consists of*R*-scalar multiples of the identity matrix.^{[1]} - Let
*F*be a field extension of a field*k*, and*R*an algebra over*k*. Then Z(*R*⊗_{k}*F*) = Z(*R*) ⊗_{k}*F*. - The centre of the universal enveloping algebra of a Lie algebra plays an important role in the representation theory of Lie algebras. For example, a Casimir element is an element of such a centre that is used to analyze Lie algebra representations. See also:
*Harish-Chandra isomorphism*. - The centre of a simple algebra is a field.

**^**"vector spaces – A linear operator commuting with all such operators is a scalar multiple of the identity".*Math.stackexchange.com*. Retrieved 2017-07-22.

- Bourbaki,
*Algebra* - Pierce, Richard S. (1982),
*Associative algebras*, Graduate texts in mathematics, vol. 88, Springer-Verlag, ISBN 978-0-387-90693-5