International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 811-812
Research notes

Norms in finite galois extensions of the rationals

Hans Opolka

Mathematisches Institut, Universität Göttingen, Bunsenstrasse 3-5, Göttingen D-3400, Germany

Received 22 August 1989; Revised 12 December 1989

Copyright © 1990 Hans Opolka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show that under certain conditions a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals.