\begin{definition}[Definition:Inverse (Abstract Algebra)/Inverse]
Let $\struct {S, \circ}$ be an algebraic structure with an identity element $e_S$.
Let $x, y \in S$ be elements.
The element $y$ is an '''inverse of $x$''' {{iff}}:
:$y \circ x = e_S = x \circ y$
that is, {{iff}} $y$ is both:
:a left inverse of $x$
and:
:a right inverse of $x$.
\end{definition}