becher@maths.ucd.ie

Submission: 2005, Jan, 26

In this article weakly isotropic quadratic forms over a (formally) real field are studied. Conditions on the field are given which imply that every weakly isotropic form over that field has a weakly isotropic subform of small dimension. Fields over which every quadratic form can be decomposed into an orthogonal sum of a strongly anisotropic form and a torsion form are characterized in different ways.

2000 Mathematics Subject Classification: 11E04, 11E81, 12D15

Keywords and Phrases: quadratic form, weakly isotropic, strongly anisotropic, real field, Pythagoras number, field invariants, SAP-field, local-global principle

Full text: dvi.gz 22 k, dvi 52 k, ps.gz 509 k, pdf.gz 128 k, pdf 143 k.

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