Jump to content

Center (ring theory)

From Wikipedia, the free encyclopedia
(Redirected from Centre of a ring)

In algebra, the center 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 "center".

If R is a ring, then R is an associative algebra over its center. 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.

Examples[edit]

See also[edit]

Notes[edit]

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

References[edit]