论文标题
在特征2中纯粹不可分割的扩展上的四元组和八元分裂
Splitting of quaternions and octonions over purely inseparable extensions in characteristic 2
论文作者
论文摘要
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 $E$.因此，我们对BernhardMühlherr和Richard Weiss提出的问题得到了负面答案。我们根据相关规范形式的各向同性行为研究了这个问题。
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 Mühlherr and Richard Weiss. We study this question in terms of the isotropy behaviour of the associated norm forms.
