\begin{definition}[Definition:Invertible Element]
Let $\struct {S, \circ}$ be an algebraic structure which has an identity $e_S$.
If $x \in S$ has an inverse, then $x$ is said to be '''invertible for $\circ$'''.
That is, $x$ is '''invertible''' {{iff}}:
:$\exists y \in S: x \circ y = e_S = y \circ x$
\end{definition}