\begin{definition}[Definition:Commutator/Ring]
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:
:$\sqbrk {a, b} := a \circ b - b \circ a$
Category:Definitions/Ring Theory
\end{definition}