Triple linkage of quadratic Pfister forms

Adam Chapman, Andrew Dolphin, David B. Leep

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 Iqn+1F=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 char(F)≠2 and u(F) = 4 , then every three quaternion algebras share a common maximal subfield.

Original languageEnglish
Pages (from-to)435-443
Number of pages9
JournalManuscripta Mathematica
Volume157
Issue number3-4
DOIs
StatePublished - Nov 1 2018

Bibliographical note

Funding Information:
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).

Funding Information:
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).

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

  • Mathematics (all)

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