Geodesic
Quadratic forms over Quadratic Extensions of Fields with Two Quaternion Algebras
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1047-1058

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we analyze what happens with respect to quadratic forms when a square root is adjoined to a field F which has exactly two quaternion algebras. There are many such fields—the real numbers and finite extensions of the p-adic numbers being two familiar examples. For general quadratic extensions, there are many unanswered questions concerning the quadratic form structure, but for these special fields we can clear up most of them.It is assumed char F ≠ 2 and K = F (√a) where a ∊ Ḟ – Ḟ 2. Ḟ denotes the non-zero elements of F. Generally the letters a, b, c, ... and α, β, ... refer to elements from Ḟ and x, y, z, ... come from . 
Cordes, Craig M.; Jr., John R. Ramsey. Quadratic forms over Quadratic Extensions of Fields with Two Quaternion Algebras. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1047-1058. doi: 10.4153/CJM-1979-096-x
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