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In [[number theory]], an '''algebraic number field''' is a principal object of study in [[algebraic number theory]]. The alge An ''algebraic number field'' ''K'' is a finite degree [[field extension]] of the [[field (mathematics)

{{r|Algebraic number field}}

{{r|Algebraic number field}}

#Let <math>K</math> be an [[algebraic number field]]. Then the integral closure <math>o_K</math>of <math>\mathbb{Z}</math> in

{{r|Algebraic number field}}

...pace, there is an associated Artin L-function. When ''K'' and ''k'' are [[algebraic number field]]s, Artin L-functions generalize [[Dedekind zeta function]]s, which are jus

...f rings originated from the study of [[polynomial|polynomial rings]] and [[Algebraic number field|algebraic number fields]] in the second half of the nineteenth century, amo

Let ''K'' be an [[algebraic number field]], a finite [[field extension|extension]] of '''Q''', and ''E'' an elliptic

...y) is an algebraic number. Fields of algebraic numbers are also called ''[[algebraic number field]]s''.