Transversal zeros and positive semidefinite forms

  • Man-Duen Choi
  • Manfred Knebusch
  • Tsit-Yuen Lam
  • Bruce Reznick
Contributions Des Participants
Part of the Lecture Notes in Mathematics book series (LNM, volume 959)


Prime Divisor Real Point Irreducible Factor Effective Divisor Zariski Closure 
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  1. [A]
    E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Seminar, Universität Hamburg 5, 100–115 (1927).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [CL]
    M.D. Choi, T.Y. Lam, Extremal positive semidefinite forms, Math. Ann. 231, 1–18 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [CL1]
    M.D. Choi, T.Y. Lam, An old question of Hilbert, Proceedings Quadratic Form Conference 1976 (ed. G. Orzech), Queen’s Papers in Pure and Appl. Math. 46, 385–405.Google Scholar
  4. [DK]
    H. Delfs, M. Knebusch, Semialgebraic topology over a real closed field II: Basic theory of semialgebraic spaces, Math. Z. 178, 175–213 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [DK1]
    H. Delfs, M. Knebusch, On the homology of algebraic varieties over real closed fields, to appear, preprint Univ. Regensburg.Google Scholar
  6. [DE]
    D.W. Dubois, G. Efroymson, Algebraic theory of real varieties I, Studies and Essays presented to Yu-Why Chen on his sixtieth birthday (1970), 107–135.Google Scholar
  7. [E]
    G. Efroymson, Henselian fields and solid k-varieties II, Proc. Amer. Math. Soc. 35, 362–366 (1972).MathSciNetzbMATHGoogle Scholar
  8. [ELW]
    R. Elman, T.Y. Lam, A. Wadsworth, Orderings under field extensions, J. reine angew. Math. 306, 7–27 (1979).MathSciNetzbMATHGoogle Scholar
  9. [R]
    B. Reznick, Extremal psd forms with few terms, Duke Math. J. 45, 363–374 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  10. [Ri]
    J.J. Risler, Une caractérisation des idéaux des variétés algébriques réelles, C.R. Acad. Sc. Paris 271, 1171–1173 (1970).MathSciNetzbMATHGoogle Scholar
  11. [Ri1]
    J.J. Risler, Le théorème des zéros en géometrie algébrique et analytique réelles, Bull. Soc. math. France 104, 113–127 (1976).MathSciNetzbMATHGoogle Scholar
  12. [S]
    G. Stengle, A Nullstellensatz and a Positivstellensatz in semialgebraic geometry, Math. Ann. 207, 87–97 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  13. [CLR]
    M.D. Choi, T.Y. Lam, B. Reznick, A combinatorial theory for sums of squares of polynomials, in preparation.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Man-Duen Choi
    • 1
  • Manfred Knebusch
    • 2
  • Tsit-Yuen Lam
    • 3
  • Bruce Reznick
    • 4
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Fakultät für Mathematik der UniversitätRegensburgF.R.G.
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyU.S.A.
  4. 4.Department of MathematicsUniversity of IllinoisUrbanaU.S.A.

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