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COMMON SLOTS OF BILINEAR AND QUADRATIC PFISTER FORMS

Part of: Forms and linear algebraic groups Division rings and semisimple Artin rings

Published online by Cambridge University Press:  03 May 2018

ADAM CHAPMAN Open the ORCID record for ADAM CHAPMAN [Opens in a new window]
ADAM CHAPMAN*
Affiliation:
Department of Computer Science, Tel-Hai Academic College, Upper Galilee, 12208, Israel email adam1chapman@yahoo.com
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Abstract

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We show that over any field $F$ of characteristic 2 and 2-rank $n$, there exist $2^{n}$ bilinear $n$-fold Pfister forms that have no slot in common. This answers a question of Becher [‘Triple linkage’, Ann.$K$-Theory, to appear] in the negative. We provide an analogous result also for quadratic Pfister forms.

Keywords

symmetric bilinear formsquadratic formsPfister formsfields of characteristic 2valuationsquaternion algebras

MSC classification

Primary: 11E04: Quadratic forms over general fields
Secondary: 11E81: Algebraic theory of quadratic forms; Witt groups and rings 16K20: Finite-dimensional
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 38 - 47
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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