Center (ring theory)

Examples

• The center of a commutative ring R is R itself.
• The center of a skew-field is a field.
• The center of the matrix ring with entries in a commutative ring R consists of R-scalar multiples of the identity matrix.
• Let F be a field extension of a field k, and R an algebra over k. Then
• The center 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 center that is used to analyze Lie algebra representations. See also: Harish-Chandra isomorphism.
• The center of a simple algebra is a field.