Submission: 2006, Jan 17
The aim of this article is to analyse a new field invariant, relevant to (formally) real fields, defined as the supremum of the dimensions of all anisotropic, weakly isotropic quadratic forms over the field. This invariant is compared with the classical u-invariant and with the Hasse number. Furthermore, in order to be able to obtain examples of fields where these invariants take certain prescribed values, totally positive field extensions are studied.
2000 Mathematics Subject Classification: 11E04, 11E81, 12D15
Keywords and Phrases: quadratic form, weakly isotropic, totally indefinite, real field, u-invariant, Hasse number, semiordering, pythagorean closure, central simple algebra, pythagorean index, Merkurjev method
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