Splitting quaternion algebras defined over a finite field extension

Karim Johannes Becher; Fatma Kader Bingöl; David B. Leep

doi:10.1142/S021949882250061X

Splitting quaternion algebras defined over a finite field extension

Karim Johannes Becher, Fatma Kader Bingöl, David B. Leep

Mathematics

Producción científica: Article › revisión exhaustiva

1 Cita (Scopus)

Resumen

We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence we obtain that every central simple algebra of degree 16 is split by a 2-extension of degree at most 216.

Idioma original	English
Número de artículo	2250061
Publicación	Journal of Algebra and its Applications
Volumen	21
N.º	3
DOI	https://doi.org/10.1142/S021949882250061X
Estado	Published - mar 1 2022

Nota bibliográfica

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Financiación

This work was supported by the FWO Odysseus program (project Explicit Methods in Quadratic Form Theory), funded by the Fonds Wetenschappelijk Onderzoek - Vlaanderen.

Financiadores	Número del financiador
Fonds Wetenschappelijk Onderzoek Vlaanderen
Fonds Wetenschappelijk Onderzoek

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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AB - We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence we obtain that every central simple algebra of degree 16 is split by a 2-extension of degree at most 216.

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KW - characteristic two

KW - corestriction

KW - exponent

KW - index

KW - quaternion algebra

KW - splitting field

KW - system of quadratic forms

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Splitting quaternion algebras defined over a finite field extension

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Financiación

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