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A formal product of places of an algebraic number field, used to encode ramification data for abelian extensions of a number

Auto-populated based on [[Special:WhatLinksHere/Modulus (algebraic number theory)]]. Needs checking by a human. {{r|Algebraic number field}}

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

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<noinclude>{{Subpages}}</noinclude>The branch of algebraic number theory which studies the abelian extensions of a number field, or more gene

An invariant attached to an extension of algebraic number fields which encodes ramification data.

An algebraic number field for which the ring of integers is a polynomial ring.

...ted in algebraic number theory, performing sophisticated computations in [[algebraic number field]]s, in [[Global field|global]] [[function field]]s, and in [[local fi ...k | author=J. Graf von Schmettow | title=KANT — a tool for computations in algebraic number fields | booktitle=Computational number theory | publisher=de Gruyter | yea

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

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...thor=A. Fröhlich | authorlink=Ali Fröhlich | coauthors=M.J. Taylor | title=Algebraic number theory | series=Cambridge studies in advanced mathematics | volume=27 | pub *{{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebraic number theory | publisher=[[Springer-Verlag]] | isbn=0-387-94225-4 | year=1986 }}

| title = Algebraic Number Theory

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Auto-populated based on [[Special:WhatLinksHere/Discriminant of an algebraic number field]]. Needs checking by a human. {{r|Algebraic number field}}

In [[algebraic number theory]], the '''genus field''' ''G'' of a [[number field]] ''K'' is the [[ * {{cite book | last=Ishida | first=Makoto | title=The genus fields of algebraic number fields | series=Lecture Notes in Mathematics | publisher=[[Springer Verlag]

...lgebraic, but the converse need not hold. For example, the field of all [[algebraic number]]s over '''Q''' is an algebraic extension but not of finite degree.

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