Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transfer of quadratic forms and of quaternion algebras over quadratic
  field extensions   A theorem of Albert-Draxl states that if a tensor product of two quaternion
division algebras $Q_1$, $Q_2$ over a field $F$ is not a division algebra, then
there exists a separable quadratic extension of $F$ that embeds as a subfield
in $Q_1$ and in $Q_2$. 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 $\varphi$
over a quadratic extension is isotropic for a linear functional $s$ such that
$s(1)=0$, then $\varphi$ contains a nondegenerate subform defined over the base
field.

5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th