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An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras
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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BibTeX
@misc{nokhodkar2026elementary,
title = {{An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras}},
author = {Amir Hossein Nokhodkar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05120},
eprint = {2610.05120},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05120},
}
RIS
TY - UNPB
TI - An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras
AU - Amir Hossein Nokhodkar
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05120
UR - https://arxiv.org/abs/2610.05120
AB - 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.
ER -