Grunwald–Wang theorem
id:
grunwald-wang-theorem-293-12044058
title:
Grunwald–Wang theorem
text:
In algebraic number theory, the Grunwald–Wang theorem is a local-global principle stating that—except in some precisely defined cases—an element x in a number field K is an nth power in K if it is an nth power in the completion K p for all but finitely many primes p of K. For example, a rational number is a square of a rational number if it is a square of a p-adic number for almost all primes p. It was introduced by Wilhelm Grunwald (1933), but there was a mistake in this original version that w
brand slug:
wiki
category slug:
encyclopedia
description:
Local-global result for when an element in a number field is an nth power
original url:
https://en.wikipedia.org/wiki/Grunwald%E2%80%93Wang_theorem
date created:
date modified:
2024-03-05T05:27:54Z
main entity:
{"identifier":"Q5612159","url":"https://www.wikidata.org/entity/Q5612159"}
image:
fields total:
13
integrity:
14