Kronecker–Weber theorem
id:
kronecker-weber-theorem-318-6160045
title:
Kronecker–Weber theorem
text:
In algebraic number theory, it can be shown that every cyclotomic field is an abelian extension of the rational number field Q, having Galois group of the form × . The Kronecker–Weber theorem provides a partial converse: every finite abelian extension of Q is contained within some cyclotomic field. In other words, every algebraic integer whose Galois group is abelian can be expressed as a sum of roots of unity with rational coefficients. For example, The theorem is named after Leopold Kronecker
brand slug:
wiki
category slug:
encyclopedia
description:
Every finite abelian extension of Q is contained within some cyclotomic field
original url:
https://en.wikipedia.org/wiki/Kronecker%E2%80%93Weber_theorem
date created:
date modified:
2022-01-28T04:42:48Z
main entity:
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image:
fields total:
13
integrity:
14