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Mathematische Zeitschrift

, Volume 239, Issue 3, pp 563–577 | Cite as

Sums of even powers in Archimedean rings

  • Jean-Philippe Monnier
  • Ronan Quarez
Original article

Abstract.

This note is devoted to the study of totally archimedean rings of regular functions. We extend Schmüdgen's theorem to this class of rings. Moreover, we show that, in such rings, every totally positive element is a sum of even powers of totally positive elements, and hence is a sum of even powers of units.

Mathematics Subject Classification (1991): 11E25, 14P99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean-Philippe Monnier
    • 1
  • Ronan Quarez
    • 2
  1. 1.Département de Mathématiques, Université d'Angers, 2, Bd. Lavoisier, 49045 Angers Cedex 01, France (e-mail : monnier@tonton.univ-angers.fr) FR
  2. 2.IRMAR (CNRS, URA 305), Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France (e-mail: quarez@maths.univ-rennes1.fr) FR

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