Noncommutative Ring

A noncommutative ring R is a ring in which the law of multiplicative commutativity is not satisfied, i.e.,


for any two elements a,b in R. In such a case, the elements a and b of the ring R are said not to commute. An important example of a noncommutative ring is the ring M_n(K) consisting of all n×n matrices whose elements are members of the field K.

See also

Commutative Ring, Ring

This entry contributed by Viktor Bengtsson

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Bengtsson, Viktor. "Noncommutative Ring." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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