Definition:Commutator/Ring

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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:

$\left[{a, b}\right] := a \circ b - b \circ a$