Pythagorean fields and the Kaplansky radical

DOI10.1016/0021-8693(79)90291-6zbMath0429.10013OpenAlexW2021663037MaRDI QIDQ1137607

Lawrence Berman

Publication date: 1979

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(79)90291-6

zbMATH Keywords

quadratic formspace of orderingsnonformally real fieldspythagorean fieldsnorm mapKaplansky radical

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15)

Related Items (3)

The Kaplansky radical of a quadratic field extension ⋮ Witt rings and Brauer groups under multiquadratic extensions. II ⋮ Formally real fields, pythagorean fields, C-fields and W-groups

Cites Work

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• Quadratic forms under algebraic extensions
• Über die Anzahl der Anordnungen eines kommutativen Körpers
• Characterizing reduced Witt rings of fields
• On the theory of quadratic forms over formally real fields
• Non-real fields \(k\) and infinite dimensional \(k\)-vectorspaces. (Quadratic forms and linear topologies. II)
• The Witt Ring of a Space of Ordering
• Spaces of Orderings IV
• Quadratic forms over fields with finite square class number
• Kaplanaky's radical and quadratic forms over non-real fields
• Quadratic forms ‘à la’ local theory
• Fröhlich's local quadratic forms.
• Quadratic Forms Over Formally Real Fields and Pythagorean Fields

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