2015•Journal of Algebra and Its ApplicationsRequires access

Non-hyperbolic splitting of quadratic pairs

Karim Johannès Becher, Andrew E. Dolphin

Abstract

We show that a non-hyperbolic quadratic pair on a central simple algebra Brauer equivalent to a quaternion algebra stays non-hyperbolic over some splitting field of the quaternion algebra. This extends a result previously only known for fields of characteristic different from two. Our presentation is free from restrictions on the characteristic of the base field.

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Key concepts: Mathematics, Quaternion algebra, Quaternion, Quadratic equation, Central simple algebra, Pure mathematics, Simple (philosophy), Algebra over a field