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👉 In mathematics, a noncommutative ring is a ring in which the commutator of two elements (a
b) and (b
c) is not equal to the product of these two elements. The commutator of two elements a and b is defined as ab - ba. Noncommutative rings are important because they allow for more flexibility with operations, such as addition and multiplication, than do commutative rings. They also have applications in various fields such as algebra

noncommunally