Commutative monoid

This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
VIEW: Definitions built on this | Facts about this: (facts closely related to Commutative monoid, all facts related to Commutative monoid) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a complete list of semi-basic definitions on this wiki

Definition

A monoid in which all elements commute is called a commutative monoid. That is, a commutative monoid satisfies $ab=ba$ for all $a,b$ in the monoid.

Related notions

Weaker than

For a monoid with all elements invertible, i.e. a group, the related notion is an abelian group.

Examples

• Any abelian group.

• The additive monoid of natural numbers.