Hereditarily non-pythagorean fields

David Grimm; David B. Leep

doi:10.1016/j.jalgebra.2021.01.013

Hereditarily non-pythagorean fields

David Grimm, David B. Leep

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	434-452
Number of pages	19
Journal	Journal of Algebra
Volume	574
DOIs	https://doi.org/10.1016/j.jalgebra.2021.01.013
State	Published - May 15 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Funding

We thank Karim Becher, Eberhard Becker, and Parul Gupta for useful conversations on these topics. Financial support by CONICYT (proyecto FONDECYT 11150956 ) and by the Universidad de Santiago de Chile (USACH) (proyecto DICYT, Codigo 041933G ) are gratefully acknowledged.

Funders	Funder number
Universidad de Santiago de Chile	041933G
Comisión Nacional de Investigación Científica y Tecnológica
Fondo Nacional de Desarrollo Científico y Tecnológico	11150956

Keywords

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

Access to Document

10.1016/j.jalgebra.2021.01.013

Cite this

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AB - 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.

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KW - Pythagorean field

KW - Quadratic closure

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KW - Sums of squares

KW - Valuations

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Hereditarily non-pythagorean fields

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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