We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence we obtain that every central simple algebra of degree 16 is split by a 2-extension of degree at most 216.

中文翻译：

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在有限域扩展上定义的分裂四元数代数

我们研究场上的二次型系统及其各向同性2- 扩展。我们应用它来获得在有限域扩展上定义的四元数代数的特定分裂域。因此，我们得到每个中心简单的度代数16被一个2- 最多扩展学位216.