---
tag: JSP0KFY52S
kind: concept
name: Presentation of a monoid
aliases: [finitely-presented-monoid, monoid-presentation, presentation-of-a-semigroup, presentation-of-inverse-semigroups-and-inverse-monoid]
sources:
  - wikipedia: en:6730121@r1278687205
    locator: Presentation of a monoid
    note: adopted
    mention: wikipedia://en/6730121
    sections: [Summary]
same_as:
  wikidata: Q7240991
  wikipedia: Presentation of a monoid
inventory: [1NKXHBF2WY]
---

## Summary

In algebra, a **presentation of a monoid** (or a **presentation of a semigroup**) is a description of a [[monoid|0N6R902FG1]] (or a [[semigroup|0XMEM406JM]]) 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.