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Homemonoid

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# monoid

A monoid is a semigroup $G$ which contains an identity element; that is, there exists an element $e\in G$ such that $e\cdot a=a\cdot e=a$ for all $a\in G$.

If $e$ and $f$ are identity elements of a monoid $G$, then $e=e\cdot f=f\cdot e=f$, so we may speak of “the” identity element of $G$.

A *monoid homomorphism* from monoids $G$ to $H$ is a semigroup homomorphism $f:G\to H$ such that $f(e_{G})=e_{H}$, where $e_{G},e_{H}$ are identity elements of $G$ and $H$ respectively.

Defines:

monoid homomorphism

Related:

Semigroup

Synonym:

homomorphism

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

20M99*no label found*34-01

*no label found*

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new question: Scheduling Algorithm by ncovella

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