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 language | English |
|---|---|
| Pages (from-to) | 435-443 |
| Number of pages | 9 |
| Journal | Manuscripta Mathematica |
| Volume | 157 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - Nov 1 2018 |
Bibliographical note
Publisher Copyright:© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
Funding
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). 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).
| Funders | Funder number |
|---|---|
| Automorphism groups of locally finite trees | G011012 |
| F.W.O. Vlaanderen | |
| F.W.O.? | |
| Research Foundation, Flanders, Belgium |
ASJC Scopus subject areas
- General Mathematics