Search results

{{r|Modulus (algebraic number theory)}}

...n of the rational numbers of finite degree; a principal object of study in algebraic number theory.

...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]

Roots of unity are clearly [[algebraic number]]s, and indeed [[algebraic integer]]s. It is often convenient to identify

An invariant attached to an extension of algebraic number fields which describes the geometric structure of the ring of integers and

{{r|Algebraic number field}} {{r|Algebraic number}}

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 pol

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

...ink=J. W. S. Cassels | coauthors=[[Albrecht Fröhlich|A. Fröhlich]] | title=Algebraic Number Theory | publisher=[[Academic Press]] | year=1967 | isbn=012268950X }} * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}

...ink=J. W. S. Cassels | coauthors=[[Albrecht Fröhlich|A. Fröhlich]] | title=Algebraic Number Theory | publisher=[[Academic Press]] | year=1967 | isbn=012268950X }} * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}

{{r|Algebraic number}}

{{r|Algebraic number field}} {{r|Algebraic number}}

In [[mathematics]], and more specifically—in [[number theory]], an '''algebraic number''' is a [[complex number]] that is a root of a [[polynomial]] with [[ration ...s that ensued forms the foundation of modern [[algebraic number theory]]. Algebraic number theory is now an immense field, and one of current research, but so far has

{{r|Algebraic number}}

{{r|Algebraic number field}} {{r|Algebraic number}}

{{r|Algebraic number}}

{{r|Discriminant of an algebraic number field}}

{{r|Algebraic number}}

...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 ' * {{cite book | author=Pierre Samuel | authorlink=Pierre Samuel | title=Algebraic number theory | publisher=Hermann/Kershaw | year=1972 }}

...], 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 fiel