Noncommutative Ring

A noncommutative ring is a mathematical structure where you can add and multiply elements, similar to numbers, but unlike regular numbers, the order of multiplication matters. For instance, in such a ring, multiplying element A by B might give a different result than multiplying B by A. This property contrasts with ordinary integers, where multiplication is commutative (A×B = B×A). Noncommutative rings are useful in advanced mathematics and physics, including quantum mechanics, because they can model systems where operations depend on order.