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

被引：0

作者：

Karim Johannes Becher

Nicolas Grenier-Boley

Jean-Pierre Tignol

机构：

[1] Universiteit Antwerpen,Departement Wiskunde en Informatica

[2] LDAR (EA4434),ICTEAM Institute

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[4] UCP,undefined

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[6] UPEC,undefined

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[8] Université de Rouen Normandie,undefined

[9] Université Catholique de Louvain,undefined

来源：

Archiv der Mathematik | 2018年 / 111卷

关键词：

Isotropy; Witt index; Corestriction; Albert form; Characteristic two; 11E04; 11E81; 12G05; 16H05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：135 / 143

页数：8

共 5 条

[1] Becher K-J(2018)Involutions and stable subalgebras J. Algebra 493 381-409
[2] Grenier-Boley N(1993)Sur la forme d’Albert et le produit tensoriel de deux algèbres de quaternions Bull. Soc. Math. Belg. Sér. B 45 333-337
[3] Tignol J-P(1993)Sur les produits tensoriels de deux algèbres de quaternions Bull. Soc. Math. Belg. Sér. B 45 329-331
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