Abstract Let F be a field, Let further D1, D2 be biquaternion algebras over F with Albert forms We prove that the dimension of anisotropic part of the form is at most 24, provided there exists a common splitting field of degree for D1 and D2. We also investigate the symbol length of i.e., the minimal number n such that is the sum of n 4-fold Pfister forms over F modulo It turns out that if is a biquaternion algebra as well, then and this inequality is strict. Among negative results we give examples of biquaternion division algebras D1, D2 without common quadratic subfield, and such that is a biquaternion algebra.

中文翻译：

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两个 Albert 形式的张量积的某些性质

摘要 设 F 为域，进一步设 D1、D2 为带 Albert 形式的 F 上的双四元数代数 我们证明了形式的各向异性部分的维数至多为 24，条件是 D1 和 D2 存在一个公共的度数分裂域。我们还研究了符号长度，即最小数 n，它是 F 模上的 n 个 4 重 Pfister 形式的总和。事实证明，如果也是一个双四元数代数，那么这个不等式是严格的。在否定结果中，我们给出了没有共同二次子域的双四元数除法代数 D1、D2 的例子，这是一个双四元数代数。