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
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