Number field

This article defines a field property: a property that can be evaluated to true/false for any field.
View a complete list of field properties|View a complete list of field extension properties

Definition

A number field is a field that is a finite extension of the field of rational numbers.

Relation with other properties

Stronger properties

• Galois number field

Metaproperties

Subfield-closedness

This field property is closed under taking subfields. In other words, any subfield of a field with this property also has this property.
View other subfield-closed field properties

A subfield of a number field is again a number field.

If $K_{1}$ and $K_{2}$ are subfields of a field $K$, and both $K_{1}$ and $K_{2}$ are number fields, then so is the composite field $K_{1}K_{2}$.

Finite-extension-closedness

This field property is closed under taking finite extensions. In other words, any finite extension of a field with this property also has this property.
View other such properties

Any finite extension of a number field is a number field.