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.
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