# Definition:Commutator/Ring

## Definition

Let $\struct {R, +, \circ}$ be a ring.

Let $a, b \in R$.

The commutator of $a$ and $b$ is the operation:

$\sqbrk {a, b} := a \circ b + \paren {-b \circ a}$

or more compactly:

$\sqbrk {a, b} := a \circ b - b \circ a$