Presentation of a monoid

Summary

In algebra, a presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set $\Sigma$ of generators and a set of relations on the free monoid $\Sigma^{\ast}$ (or the free semigroup $\Sigma^{+}$) generated by $\Sigma$. The monoid is then presented as the quotient of the free monoid (or the free semigroup) by these relations. This is an analogue of a group presentation in group theory.