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

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Article number	2250061
Journal	Journal of Algebra and its Applications
Volume	21
Issue number	3
DOIs	https://doi.org/10.1142/S021949882250061X
State	Published - Mar 1 2022

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Funding

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

Funders	Funder number
Fonds Wetenschappelijk Onderzoek Vlaanderen
Fonds Wetenschappelijk Onderzoek

Keywords

2 -extension
Central simple algebra
characteristic two
corestriction
exponent
index
quaternion algebra
splitting field
system of quadratic forms

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

Access to Document

10.1142/S021949882250061X

Cite this

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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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Splitting quaternion algebras defined over a finite field extension

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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