Center (ring theory)

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.This algebra-related article is a stub.You can help Wikipedia by expanding it.
algebrasubringcommutative ringassociative algebraskew-fieldmatrix ringidentity matrixfield extensionuniversal enveloping algebraLie algebrarepresentation theory of Lie algebrasCasimir elementLie algebra representationsHarish-Chandra isomorphismsimple algebraCenter of a groupCentral simple algebraMorita equivalence