\begin{definition}[Definition:Cancellable Operation]
Let $\struct {S, \circ}$ be an algebraic structure.
The operation $\circ$ in $\struct {S, \circ}$ is '''cancellable''' {{iff}}:
:$\forall a, b, c \in S: a \circ b = a \circ c \implies b = c$
:$\forall a, b, c \in S: a \circ c = b \circ c \implies a = b$
That is, {{iff}} it is both a left cancellable operation and a right cancellable operation.
\end{definition}