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
[3] UA,undefined
[4] UCP,undefined
[5] UPD,undefined
[6] UPEC,undefined
[7] URN,undefined
[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
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页码:135 / 143
页数:8
相关论文
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
  • [4] Knus M-A(undefined)undefined undefined undefined undefined-undefined
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