Definition:Commutator/Ring

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Let $a, b \in R$.

The commutator of $a$ and $b$ is the operation:
 * $\left[{a, b}\right] := a \circ b + \left({- b \circ a}\right)$

or more compactly:
 * $\left[{a, b}\right] := a \circ b - b \circ a$