A noncommutative ring 
is a ring in which multiplication
is not commutative, i.e.,
 |
for some two elements 
. Such elements 
and 
are said not to commute. An example is the ring 
of all 
matrices over a field 
for 
.
Noncommutative Ring
See also
Commutative Ring, RingPortions of this entry contributed by Viktor Bengtsson
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Cite this as:
Weisstein, Eric W., with contributions by Viktor Bengtsson. "Noncommutative Ring." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NoncommutativeRing.html