Hereditarily Non-Pythagorean Fields - Grimm, D (Academic Press, 2021)
We prove for a large class of fields F that every proper finite extension of Fpyth, the pythagorean closure of F, is not a pythagorean field. This class of fields contains number fields and fields F that are finitely generated of transcendence degree at least one over some subfield of F. © 2021 Elsevier Inc.