Multiplicative monoid of non-zero integers

This article is about a particular monoid, i.e., a field unique up to isomorphism. View a complete list of particular monoids

Definition

• This monoid is the set of non-zero integers under multiplication.

This monoid may be denoted $({\mathbb{Z}}^{\times },\times )$, $(\mathbb{Z}{,}^{\times }\cdot )$, or simply as ${\mathbb{Z}}^{\times }$.

Monoid properties

Property	Satisfied	Explanation
Commutative monoid	Yes	Multiplication of integers is commutative

See also

For the usual larger sets of numbers which the integers are embedded in, the related construction becomes a group:

• Multiplicative group of non-zero complex numbers
• Multiplicative group of non-zero real numbers
• Multiplicative group of non-zero real algebraic numbers
• Multiplicative group of non-zero rational numbers

Also see additive group of integers.