Hereditarily non-pythagorean fields

2 Jan 2020 · David Grimm, David B. Leep ·

We prove for a large class of fields $F$ that every proper finite extension of $F_{pyth}$, 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 $F$.