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arXiv · 2012.09644

Splitting of quaternions and octonions over purely inseparable extensions in characteristic 2

Detlev W. Hoffmann
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Abstract

We give examples of quaternion and octonion division algebras over a field $F$ of characteristic $2$ that split over a purely inseparable extension $E$ of $F$ of degree $\geq 4$ but that do not split over any subextension of $F$ inside $E$ of lower exponent, or, in the case of octonions, over any simple subextension of $F$ inside $E$. Thus, we get a negative answer to a question posed by Bernhard M\"uhlherr and Richard Weiss. We study this question in terms of the isotropy behaviour of the associated norm forms.

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Detlev W. Hoffmann. 2020-12-15. Splitting of quaternions and octonions over purely inseparable extensions in characteristic 2. https://arxiv.org/abs/2012.09644

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