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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Witt kernels of bilinear forms for algebraic extensions in characteristic $2$
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by Detlev W. Hoffmann PDF
Proc. Amer. Math. Soc. 134 (2006), 645-652 Request permission

Abstract:

Let $F$ be a field of characteristic $2$ and let $K/F$ be a purely inseparable extension of exponent $1$. We determine the kernel $W(K/F)$ of the natural restriction map $WF\to WK$ between the Witt rings of bilinear forms of $F$ and $K$, respectively. This complements a result by Laghribi who computed the kernel for the Witt groups of quadratic forms for such an extension $K/F$. Based on this result, we will determine $W(K/F)$ for a wide class of finite extensions which are not necessarily purely inseparable.
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Additional Information
  • Detlev W. Hoffmann
  • Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • Email: detlev.hoffmann@nottingham.ac.uk
  • Received by editor(s): October 10, 2004
  • Published electronically: August 29, 2005
  • Additional Notes: The research on this paper was supported in part by the European research network HPRN-CT-2002-00287 “Algebraic $K$-Theory, Linear Algebraic Groups and Related Structures”.

  • Dedicated: In memory of Professor Martin Kneser
  • Communicated by: Bernd Ulrich
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 645-652
  • MSC (2000): Primary 11E04; Secondary 11E81, 12F15
  • DOI: https://doi.org/10.1090/S0002-9939-05-08175-X
  • MathSciNet review: 2180880