Definition:Monoid

Definition
A monoid is a semigroup with an identity element.

Monoid Axioms
The properties that define a monoid can be gathered together as follows:

A monoid can not be empty, because it must at least have an identity.

Also see

 * Identity of Semigroup is Unique: in a monoid there is only one identity element.


 * Definition:Monoid Category, modelling monoids in category theory.