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In [[mathematics]], a '''monogenic field''' is an [[algebraic number field]] for which there exists an element In a monogenic field ''K'', the [[Discriminant of an algebraic number field|field discriminant]] of ''K'' is equal to the [[discriminant of a polynomia

An element of an algebraic number field which has a denominator confined to primes in some fixed set.

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...field''' is an invariant attached to an [[field extension|extension]] of [[algebraic number field]]s which describes the geometric structure of the [[ring of integers]] and

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...c embedding of the generators of the unit group of the maximal order of an algebraic number field.

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...], the '''different ideal''' is an invariant attached to an extension of [[algebraic number field]]s. ...tive norm]] of the relative different is equal to the [[Discriminant of an algebraic number field|relative discriminant]] Δ_''L''/''K''. In a tower of fields ''L

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...e of integral closure is the [[ring of integers]] or maximal order in an [[algebraic number field]] ''K'', which may be defined as the integral closure of '''Z''' in ''K''.

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In [[mathematics]], to each [[algebraic number field]] ''k'', there is associated an important function called the '''Dedekind z If ''k'' is an algebraic number field, the Dedekind zeta function of the field is a [[meromorphic function]], def

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...'''cycle''') is a formal product of [[Place (mathematics)|place]]s of an [[algebraic number field]]. It is used to encode [[ramification]] data for [[abelian extension]]s o Let ''K'' be an algebraic number field with ring of integers ''R''. A ''modulus'' is a formal product

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