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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.
^Book and Otto, Theorem 7.1.7, p. 149
and 23 Related for: Presentation of a monoid information
In abstract algebra, a branch of mathematics, amonoid is a set equipped with an associative binary operation and an identity element. For example, the...
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obtain apresentationof the bicyclic monoid. Thus semi-Thue systems constitute a natural framework for solving the word problem for monoids and groups...
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group Group ring Group with operators Heap Linear algebra Magma Module MonoidMonoid ring Quandle Quasigroup Quantum group Ring Semigroup Vector space Affine...
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(the Wirtinger presentation) in which the relations only involve conjugation. So, this presentation can also be used as apresentationofa quandle. The...
201–215, doi:10.1023/A:1015632704977, S2CID 18334698. Duncan, A. J.; Robertson, E. F.; Ruskuc, N. (1999), "Automatic monoids and change of generators", Mathematical...
words in A {\displaystyle A} and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A {\displaystyle...
{\displaystyle N} (respecting the group, or even just monoid structure) is the same thing as a functor F : B H → C a t {\displaystyle F:BH\to Cat} from the groupoid...
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