Presentation of a monoid

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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 Σ of generators and a set of relations on the free monoid Σ^∗ (or the free semigroup Σ⁺) generated by Σ. 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.

As a mathematical structure, a monoid presentation is identical to a string rewriting system (also known as a semi-Thue system). Every monoid may be presented by a semi-Thue system (possibly over an infinite alphabet).^[1]

A presentation should not be confused with a representation.