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Triple linkage of quadratic Pfister forms

(2018) MANUSCRIPTA MATHEMATICA. 157(3-4). p.435-443
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Organization
Abstract
Given a field F of characteristic 2, we prove that if every three quadratic nfold Pfister forms have a common quadratic (n - 1)- fold Pfister factor then I n+ 1 q 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 char(F) = 2 and u(F) = 4, then every three quaternion algebras share a common maximal subfield.
Keywords
QUATERNION ALGEBRAS, U-INVARIANT

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Citation

Please use this url to cite or link to this publication:

MLA
Chapman, Adam, Andrew Dolphin, and David B Leep. “Triple Linkage of Quadratic Pfister Forms.” MANUSCRIPTA MATHEMATICA 157.3-4 (2018): 435–443. Print.
APA
Chapman, A., Dolphin, A., & Leep, D. B. (2018). Triple linkage of quadratic Pfister forms. MANUSCRIPTA MATHEMATICA, 157(3-4), 435–443.
Chicago author-date
Chapman, Adam, Andrew Dolphin, and David B Leep. 2018. “Triple Linkage of Quadratic Pfister Forms.” Manuscripta Mathematica 157 (3-4): 435–443.
Chicago author-date (all authors)
Chapman, Adam, Andrew Dolphin, and David B Leep. 2018. “Triple Linkage of Quadratic Pfister Forms.” Manuscripta Mathematica 157 (3-4): 435–443.
Vancouver
1.
Chapman A, Dolphin A, Leep DB. Triple linkage of quadratic Pfister forms. MANUSCRIPTA MATHEMATICA. 2018;157(3-4):435–43.
IEEE
[1]
A. Chapman, A. Dolphin, and D. B. Leep, “Triple linkage of quadratic Pfister forms,” MANUSCRIPTA MATHEMATICA, vol. 157, no. 3–4, pp. 435–443, 2018.
@article{8619315,
  abstract     = {Given a field F of characteristic 2, we prove that if every three quadratic nfold Pfister forms have a common quadratic (n - 1)- fold Pfister factor then I n+ 1 q 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 char(F) = 2 and u(F) = 4, then every three quaternion algebras share a common maximal subfield.},
  author       = {Chapman, Adam and Dolphin, Andrew and Leep, David B},
  issn         = {0025-2611},
  journal      = {MANUSCRIPTA MATHEMATICA},
  keywords     = {QUATERNION ALGEBRAS,U-INVARIANT},
  language     = {eng},
  number       = {3-4},
  pages        = {435--443},
  title        = {Triple linkage of quadratic Pfister forms},
  url          = {http://dx.doi.org/10.1007/s00229-017-0996-6},
  volume       = {157},
  year         = {2018},
}

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