Hasse norm theorem
id:
hasse-norm-theorem-262-7992087
title:
Hasse norm theorem
text:
In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K is a local norm everywhere, then it is a global norm.
Here to be a global norm means to be an element k of K such that there is an element l of L with N L / K ( l ) = k ; in other words k is a relative norm of some element of the extension field L. To be a local norm means that for some prime p of K and some prime P of L lying over K, then k is a norm from LP; here t
brand slug:
wiki
category slug:
encyclopedia
description:
In cyclic extension of number fields, if k is a local norm everywhere, it is a global norm
original url:
https://en.wikipedia.org/wiki/Hasse_norm_theorem
date created:
date modified:
2023-06-04T13:08:56Z
main entity:
{"identifier":"Q3527209","url":"https://www.wikidata.org/entity/Q3527209"}
image:
fields total:
13
integrity:
14