Abstract
Given a field F of characteristic 2, we prove that if every three quadratic n-fold Pfister forms have a common quadratic \((n-1)\)-fold Pfister factor then \(I_q^{n+1} F=0\). As a result, we obtain that if every three quaternion algebras over F share a common maximal subfield then u(F) is either 0, 2 or 4. We also prove that if F is a nonreal field with \({\text {char}}(F) \ne ~2\) and \(u(F)=4\), then every three quaternion algebras share a common maximal subfield.
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Acknowledgements
We thank the referee for useful suggestions that improved the clarity of the paper. The second author was supported by Automorphism groups of locally finite trees (G011012) with the Research Foundation, Flanders, Belgium (F.W.O. Vlaanderen).
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Chapman, A., Dolphin, A. & Leep, D.B. Triple linkage of quadratic Pfister forms. manuscripta math. 157, 435–443 (2018). https://doi.org/10.1007/s00229-017-0996-6
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DOI: https://doi.org/10.1007/s00229-017-0996-6