##### Wiktionary

**algebraic number field**

n. (context algebra field theory English) number field

##### Wikipedia

**Algebraic number field**

In mathematics, an **algebraic number field** (or simply **number field**) *F* is a finite degree (and hence algebraic) field extension of the field of rational numbers **Q**. Thus *F* is a field that contains **Q** and has finite dimension when considered as a vector space over **Q**.

The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.