English

Hereditarily non-pythagorean fields

Number Theory 2021-02-02 v2

Abstract

We prove for a large class of fields FF that every proper finite extension of FpythF_{pyth}, the pythagorean closure of FF, is not a pythagorean field. This class of fields contains number fields and fields FF that are finitely generated of transcendence degree at least one over some subfield of FF.

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

R2 v1 2026-06-23T13:01:47.618Z