Pythagorean \(*\)-fields

DOI10.1006/jabr.1999.8149zbMath0983.12001OpenAlexW4210515387MaRDI QIDQ1972047

Tara L. Smith, Thomas C. Craven

Publication date: 13 August 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8149

zbMATH Keywords

signatureHermitian formsvaluationWitt groupsspace of orderingsBaer orderingsformally real \(S\)-fieldformally real strongly Pythagorean \(*\)-fieldsstrongly Pythagorean division ringstotal semisignature mappingsweakly isotopic forms

Mathematics Subject Classification ID

Algebraic theory of quadratic forms; Witt groups and rings (11E81) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Bilinear and Hermitian forms (11E39) Skew fields, division rings (12E15) Ordered fields (12J15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orderings and valuations on *-fields
• Strong ordering of *-fields
• Witt groups of Hermitian forms over \(\ast\)-fields
• Orderings and square roots in \(^*\)-fields
• Central simple algebras
• Hermitian forms over ordered *-fields
• Weak \(*\)-orderings on \(*\)-fields
• Signatures on semilocal rings
• Zur Galoistheorie pythagoreischer Körper
• On sums of squares and on elliptic curves over function fields
• Approximation Properties for Orderings on ∗ -Fields
• Extending Valuations to Finite Dimensional Division Algebras
• ∗ -Valuations and Ordered ∗ -Fields
• On the Structure of Unitary Groups
• On the Structure of Unitary Groups (II)
• Quadratic forms over arbitrary fields