\begin{definition}[Definition:Free Idempotent Monoid]
Let $\left({S, \circ}\right)$ be a monoid which is generated by a set of elements, and such that:
:$\forall x \in S: x = x \circ x$
Then $\left({S, \circ}\right)$ is a '''free idempotent monoid'''.
Category:Definitions/Monoids
\end{definition}