Inventiones mathematicae

, Volume 76, Issue 1, pp 77–91 | Cite as

Bounds in the theory of polynomial rings over fields. A nonstandard approach

  • L. van den Dries
  • K. Schmidt
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References

  1. 1.
    Bourbaki, N.: Commutative algebra. Paris: Hermann 1972Google Scholar
  2. 2.
    van den Dries, L.: Model theory of fields. Thesis, Utrecht 1978Google Scholar
  3. 3.
    van den Dries, L.: Bounds and algorithms in the theory of polynomial ideals. In: Logic colloquium 1978, (Boffa, M., Van Dalen, D., McAloon, K., eds.) North-Holland 1979Google Scholar
  4. 4.
    van den Dries, L., Wilkie, A.J.: Gromov's theorem concerning groups of polynomial growth and elementary logic. To appear in J. of AlgebraGoogle Scholar
  5. 5.
    Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Math. Ann.95, 736–788 (1926)Google Scholar
  6. 6.
    Hochster, M.: Some applications of the Frobenius in characteristic 0. Bull. AMS84, 886–912 (1978)Google Scholar
  7. 7.
    Keisler, H.J.: Foundations of infinitesimal calculus. Boston: Prindle, Weber & Schmidt 1976Google Scholar
  8. 8.
    Lang, S.: Algebra. Reading, Mass.: Addison-Wesley 1965Google Scholar
  9. 9.
    Robinson, A.: Metamathematical problems. J. Symbolic Logic38, 500–516 (1973)Google Scholar
  10. 10.
    Robinson, A.: On bounds in the theory of polynomial ideals. Selected questions of algebra and logic. (A collection dedicated to the memory of A.I. Mal'cev). In: Abraham Robinson, Selected Papers, vol. 1, Model Theory and Algebra, pp. 482–489, Yale Un. Press 1979Google Scholar
  11. 11.
    Roquette, P.: Nonstandard aspects of Hilbert's Irreducibility Theorem. In: Model Theory and Algebra. A memorial Tribute to Abraham, Robinson, Saracino, D., Weispfenning, V. (eds.). Lecture Notes in Mathematics, vol. 498, pp. 231–275. Berlin-Heidelberg-New York: Springer 1975Google Scholar
  12. 12.
    Schmidt, K.: Modelltheoretische Methoden in der Algebraischen Geometrie. Diplomarbeit, Kiel 1979Google Scholar
  13. 13.
    Seidenberg, A.: Constructions in algebra. Trans. AMS197, 273–313 (1974)Google Scholar
  14. 14.
    Seidenberg, A.: Construction of the integral closure of a finite integral domain. II. Proc. AMS52, 368–372 (1975)Google Scholar
  15. 15.
    Seidenberg, A.: Constructions in a polynomial ring over the ring of integers. American J. of Math.100, 685–703 (1978)Google Scholar
  16. 16.
    Stolzenberg, G.: Constructive Normalization of an Algebraic Variety. Bull. AMS74, 595–599 (1968)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • L. van den Dries
    • 1
  • K. Schmidt
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Abteilung Logik, Philosophisches SeminarUniversität KielKielFederal Republic of Germany

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