Totally positive field extensions and the pythagorean index

DOI10.1142/s0219498824500348MaRDI QIDQ6089239

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Publication date: 14 December 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

orderinghyperbolicorthogonal involutionformally real fieldcentral simple algebraisotropicweakly hyperbolicsemiorderingpythagorean fieldweakly isotropicpythagorean indextotally positive field extension

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Algebraic theory of quadratic forms; Witt groups and rings (11E81) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Finite-dimensional division rings (16K20) Forms over real fields (11E10)

Cites Work

• Lectures on formally real fields
• A local-global principle for algebras with involution and Hermitian forms.
• Semiorderings and stability index under field extensions
• Decomposability for division algebras of exponent two and associated forms
• Totally positive extensions and weakly isotropic forms
• Hasse principles and the u-invariant over formally real fields
• Some Local-Global Principles for Formally Real Fields
• A weak Hasse principle for central simple algebras with an involution
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