karimjohannes.becher@uantwerpen.be

Submission: 2016, Oct 21

A theorem of Albert-Draxl states that if a tensor product of two quaternion division algebras Q1, Q2 over a field F is not a division algebra, then there exists a separable quadratic extension of F that embeds as a subfield in Q1 and in Q2. We establish a modified version of this result where the tensor product of quaternion algebras is replaced by the corestriction of a single quaternion algebra over a separable field extension. As a tool in the proof, we show that if the transfer of a nonsingular quadratic form \phi over a quadratic extension is isotropic for a linear functional s such that s(1)=0, then \phi contains a nondegenerate subform defined over the base field.

2010 Mathematics Subject Classification: 11E81, 11E04, 16K20, 16H05

Keywords and Phrases:

Full text: dvi.gz 16 k, dvi 33 k, ps.gz 788 k, pdf.gz 106 k, pdf 124 k.

Server Home Page