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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

A variant of a theorem by Springer


Authors: I. Panin and U. Rehmann
Original publication: Algebra i Analiz, tom 19 (2007), nomer 6.
Journal: St. Petersburg Math. J. 19 (2008), 953-959
MSC (2000): Primary 53A04; Secondary 52A40, 52A10
Published electronically: August 21, 2008
MathSciNet review: 2411641
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Abstract | References | Similar Articles | Additional Information

Abstract: The theorem in question gives a sufficient condition for a quadratic space over a local ring $ R$ to contain a hyperbolic plane over $ R$.


References [Enhancements On Off] (What's this?)

  • [La] T. Y. Lam, The algebraic theory of quadratic forms, W. A. Benjamin, Inc., Reading, Mass., 1973. Mathematics Lecture Note Series. MR 0396410 (53 #277)
  • [P] I. Panin, Rationally isotropic quadratic spaces are locally isotropic, www.math.uiuc.edu/K-theory/ 0671/2003

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Additional Information

I. Panin
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Address at time of publication: SFB-701 at Fakultät für Mathematik, Universität Bielefeld, Germany
Email: panin@pdmi.ras.ru, panin@math.uni-bielefeld.de

U. Rehmann
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Email: rehmann@math.uni-bielefeld.de

DOI: http://dx.doi.org/10.1090/S1061-0022-08-01029-7
PII: S 1061-0022(08)01029-7
Keywords: Quadratic forms, Springer's theorem, local domain
Received by editor(s): July 30, 2007
Published electronically: August 21, 2008
Additional Notes: This work is a part of the project SFB-701 at Fakultät für Mathematik, Universität Bielefeld. The first author is also supported by the Presidium of RAS Program “Fundamental Research”, an RFBR-grant, and the INTAS-05-1000008-8118 grant
Dedicated: To the memory of D. K. Faddeev
Article copyright: © Copyright 2008 American Mathematical Society