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arXiv · 2001.00618

Hereditarily non-pythagorean fields

David Grimm·David B. Leep
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Abstract

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 $F$.

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David Grimm, David B. Leep. 2021-02-01. Hereditarily non-pythagorean fields. https://doi.org/10.1016/j.jalgebra.2021.01.013

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