Hereditarily non-pythagorean fields
Number Theory
2021-02-02 v2
Abstract
We prove for a large class of fields that every proper finite extension of , the pythagorean closure of , is not a pythagorean field. This class of fields contains number fields and fields that are finitely generated of transcendence degree at least one over some subfield of .
Keywords
Cite
@article{arxiv.2001.00618,
title = {Hereditarily non-pythagorean fields},
author = {David Grimm and David B. Leep},
journal= {arXiv preprint arXiv:2001.00618},
year = {2021}
}
Comments
to appear in Journal of Algebra