Formally real fields with prescribed invariants in the theory of quadratic forms
type: Item
instance of: scholarly article
title: Formally real fields with prescribed invariants in the theory of quadratic forms
zbMATH Open document ID: 0734.11028
DOI: 10.1016/0019-3577(91)90042-6
author: E. A. M. Hornix
published in: Indagationes Mathematicae. New Series
publication date: 1991-01-01T00:00:00Z
review text: In 1989 A. Merkur'ev solved an old problem on the u-invariant constructing non-real fields F such that \(I^ 3(F)=0\) and \(u(F)=2n\), where n is any given integer \(\geq 1\). The author extends the ideas of Merkur'ev to provide the readers with examples of formally real fields \(F_ 1\) and \(F_ 2\) such that \(I_ t^ 3(F_ 1)=I_ t^ 3(F_ 2)=0\), the Hasse numbers \(\tilde u(F_ 1)\) and \(\tilde u(F_ 2)\) are equal to 2n and \(u(F_ 1)=u(F_ 2)+2=2n\). In the construction she also takes care of other invariants connected with orderings, for example \(\tilde ud(F)\) which is a counterpart of \(\tilde u(F)\) in the family of quadratic forms \(q\cong q_+\perp -q_-\) with \(q_+,q_-\) totally positive.
reviewed by: Andrzej Sładek
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 11E10
Mathematics Subject Classification ID: 12D15
zbMATH DE Number: 4214117
zbMATH Keywords: division algebra
zbMATH Keywords: Clifford algebra
zbMATH Keywords: u-invariant
zbMATH Keywords: examples of formally real fields
zbMATH Keywords: Hasse numbers
zbMATH Keywords: quadratic forms
MaRDI profile type: Publication
full work available at URL: 0019-3577(91)90042-6
OpenAlex ID: W2007486426
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description: scientific article; zbMATH DE number 4214117