Given a ring "R", let formula_45 denote the set of all elements "x" in "R" such that "x" commutes with every element in "R": formula_46 for any "y" in "R". Then formula_45 is a subring of "R", called the center of "R". More generally, given a subset "X" of "R", let "S" be the set of all elements in "R" that commute with every element in "X". Then "S" is a subring of "R", called the centralizer (or commutant) of "X". The center is the centralizer of the entire ring "R". Elements or subsets of the center are said to be "central" in "R"; they (each individually) generate a subring of the center.