Algebraic number theory

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In mathematics, an algebraic number field (or simply number field) is a finite (and therefore algebraic) field extension of the rational numbers Q. That is, it is a field which contains Q and has finite dimension when considered as a vector space over Q.

The study of algebraic number fields, and these days also of infinite algebraic extensions of the rational number field, is the central topic of algebraic number theory.

See in particular:

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