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Sums of squares in central simple algebras

Name: Sums of squares in central simple algebras
Creator: Lewis, D.W.
Keywords: 510.mathematics, Division rings and semisimple Artin rings, Finite rings and finite-dimensional associative algebras, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), sum of squares, trace form, 0101 mathematics, Skew fields, division rings, Quadratic forms over general fields, central simple algebra

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1985 Germany English Publisher:Springer Science and Business Media LLCJournal:Mathematische Zeitschrift, volume 190, pages 497-498 (issn: 0025-5874, eissn: 1432-1823,

Authors: Lewis, D.W.;

doi: 10.1007/bf01214748

Sums of squares in central simple algebras

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Abstract

Let A be a central simple algebra over a field F of characteristic not equal to two. It is proved that zero is a non-trivial sum of squares in A if and only if the trace form of A over F is weakly isotropic. This confirms a recent conjecture of Leep, Shapiro and Wadsworth.

Country

Germany

Related Organizations

University College Dublin
Ireland
DigiZeitschriften
Germany

Keywords

510.mathematics, Division rings and semisimple Artin rings, Finite rings and finite-dimensional associative algebras, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), sum of squares, trace form, Skew fields, division rings, Quadratic forms over general fields, central simple algebra, Article

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