Hereditarily non-pythagorean fields
arXiv:2001.00618 · doi:10.1016/j.jalgebra.2021.01.013
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 .
to appear in Journal of Algebra