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Concept
Algebraic number field
Summary
In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers \mathbb{Q} such that the field extension K / \mathbb{Q} has finite degree (and hence is an algebraic field extension).
Thus K is a field that contains \mathbb{Q} and has finite dimension when considered as a vector space over \mathbb{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. This study reveals hidden structures behind usual rational numbers, by using algebraic methods.
Definition
Prerequisites
Field and Vector space
The notion of algebraic number field relies on the concept of a field. A field consists of a set of elements together with two operations, namely addition, and multiplic
Official source
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