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Transfer of quadratic forms and of quaternion algebras over quadratic field extensions

Transfer of quadratic forms and of quaternion algebras over quadratic field extensions Two different proofs are given showing that a quaternion algebra Q defined over a quadratic étale extension K of a given field has a corestriction that is not a division algebra if and only if Q contains a quadratic algebra that is linearly disjoint from K. This is known in the case of a quadratic field extension in characteristic different from two. In the case where K is split, the statement recovers a well-known result on biquaternion algebras due to Albert and Draxl. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archiv der Mathematik Springer Journals

Transfer of quadratic forms and of quaternion algebras over quadratic field extensions

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0003-889X
eISSN
1420-8938
DOI
10.1007/s00013-018-1198-5
Publisher site
See Article on Publisher Site

Abstract

Two different proofs are given showing that a quaternion algebra Q defined over a quadratic étale extension K of a given field has a corestriction that is not a division algebra if and only if Q contains a quadratic algebra that is linearly disjoint from K. This is known in the case of a quadratic field extension in characteristic different from two. In the case where K is split, the statement recovers a well-known result on biquaternion algebras due to Albert and Draxl.

Journal

Archiv der MathematikSpringer Journals

Published: May 30, 2018

References