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