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

摘要

Two different proofs are given showing that a quaternion algebra Q defined over a quadratic ,tale 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.