Hereditarily non-pythagorean fields

David Grimm, David B. Leep

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)434-452
Number of pages19
JournalJournal of Algebra
StatePublished - May 15 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.


  • Function field
  • Hereditarily pythagorean
  • Number field
  • Pythagorean closure
  • Pythagorean field
  • Quadratic closure
  • Quadratically closed field
  • Sums of squares
  • Valuations

ASJC Scopus subject areas

  • Algebra and Number Theory


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