An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras

Amir Hossein Nokhodkar

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arXiv · 2610.05120

An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras

Amir Hossein Nokhodkar

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Abstract

We give a short and simple proof that an anisotropic generalized quadratic form over a quaternion division algebra with involution of the first kind, in arbitrary characteristic, remains anisotropic after scalar extension to any odd-degree field extension.

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Amir Hossein Nokhodkar. 2026-10-04. An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras. https://arxiv.org/abs/2610.05120

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