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 formula_1; "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.