## You are here

Homemonoid

## Primary tabs

# 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*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Attached Articles

## Corrections

classification by yark ✓