Let $q$ be a unimodular quadratic form over a field $K$. Pfister's famous local–global principle asserts that $q$ represents a torsion class in the Witt group of $K$ if and only if it has signature 0, and that in this case, the order of Witt class of $q$ is a power of 2. We give two analogues of this result to systems of quadratic forms, the second of which applying only to nonsingular pairs. We also prove a counterpart of Pfister's theorem for finite‐dimensional $K$‐algebras with involution, generalizing a result of Lewis and Unger.

中文翻译：

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普菲斯特的局部-整体原理和二次形式系统

让 $q$ 在一个场上是单模二次形式 $ķ$。普菲斯特著名的地方-全球原则断言：$q$ 代表维特组中的扭力类 $ķ$ 当且仅当它具有签名0，并且在这种情况下，即Witt类的顺序 $q$是2的幂。我们将这个结果的两个类似物给予二次形式的系统，其中第二个仅适用于非奇异对。我们还证明了Pfister定理的有限维对应项$ķ$-具有对合的代数，推广了Lewis和Unger的结果。