Advertisement

Variantes du Nullstellensatz réel et anneaux formellement réels

  • J.-L. Colliot-Thélène
Articles De Synthèse
Part of the Lecture Notes in Mathematics book series (LNM, volume 959)

Keywords

Symmetric Bilinear Form Arbitrary Commutative Ring Pythagoras Number Proposition Suivante Sont Identiques 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ba]
    R. BAEZA: Über die Stufe von Dedekind-Ringen, Archiv der Math. 33 (1979) p. 226–231.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [Bo]
    N. BOURBAKI: Algèbre commutative, Chap. II, Hermann, Paris (1961).zbMATHGoogle Scholar
  3. [B-E]
    J. BOCHNAK, G. EFROYMSON: Real Algebraic Geometry and the 17 th Hilbert Problem, Math. Ann. 251 (1980) p. 213–241.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [Br]
    L. BRÖCKER: Positivbereiche in kommutativen Ringen, erscheint in Abh. Math. Sem. Univ. Hamburg.Google Scholar
  5. [BDS]
    L. BRÖCKER, A. DRESS, R. SCHARLAU: An (almost) trivial local-global principle for the representation of −1 as a sum of squares in an arbitrary commutative ring (Vorabdruck).Google Scholar
  6. [CDLR]
    M. D. CHOI, Z. D. DAI, T. Y. LAM, B. REZNICK: The Pythagoras Number of Some Affine Algebras and Local Algebras (Preprint).Google Scholar
  7. [C1]
    M.-F. COSTE-ROY: Thèse, Université de Paris-Nord (1980).Google Scholar
  8. [C2]
    M. COSTE: Ensembles semi-algébriques et fonctions de Nash, Prépublication de l’Université de Paris-Nord (1981).Google Scholar
  9. [K1]
    M. KNEBUSCH: Specialization of quadratic and symmetric bilinear forms, and a norm theorem, Acta Arithmetica 24 (1973) p. 279–299.MathSciNetzbMATHGoogle Scholar
  10. [K2]
    M. KNEBUSCH: Symmetric bilinear forms over algebraic varieties, in Conference on Quadratic Forms, Queen’s papers in pure and applied Mathematics no 46 (1977) p. 103–283.Google Scholar
  11. [L]
    T. Y. LAM: The theory of ordered fields, in Ring theory and algebra III, Lecture notes in pure and applied mathematics, Vol. 55, Marcel Dekker (1980).Google Scholar
  12. [Lg]
    S. LANG: The theory of real places, Annals of Mathematics, Vol. 57 (1953) p. 378–391.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [Lo1]
    F. LORENZ: Quadratische Formen und die Artin-Schreiersche Theorie der formal reellen Körper, Bull. Soc. Math. France, Mémoire 48 (1977) p. 61–73.zbMATHGoogle Scholar
  14. [Lo2]
    F. LORENZ: Einige Bemerkungen zu einem Satz von Sylvester, Vorabdruck (1978).Google Scholar
  15. [P]
    A. PRESTEL: Lectures on formally real fields, IMPA Lecture Notes, Rio de Rio de Janeiro (1975).Google Scholar
  16. [S]
    G. STENGLE: A Nullstellensatz and a Positivstellensatz in Semialgebraic Geometry, Math. Ann. 207 (1974) p. 87–97.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J.-L. Colliot-Thélène
    • 1
  1. 1.C.N.R.S. MathématiquesUniversité de Paris-SudOrsayFrance

Personalised recommendations