The ring center 
of a ring 
is the subring of elements that
commute with every element of 
. Thus
 |
A ring is commutative iff 
.
The center of the matrix ring 
over a ring with identity consists
of scalar matrices 
with 
(Lam 2001).
The commuting graph of a noncommutative ring omits its central elements, since each would be adjacent to every other graph vertex.
