Skip to main content
SpringerLink
Log in

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

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bourbaki, N.: Commutative algebra. Paris: Hermann 1972

    Google Scholar 

  2. van den Dries, L.: Model theory of fields. Thesis, Utrecht 1978

  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 1979

  4. van den Dries, L., Wilkie, A.J.: Gromov's theorem concerning groups of polynomial growth and elementary logic. To appear in J. of Algebra

  5. Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Math. Ann.95, 736–788 (1926)

    Google Scholar 

  6. Hochster, M.: Some applications of the Frobenius in characteristic 0. Bull. AMS84, 886–912 (1978)

    Google Scholar 

  7. Keisler, H.J.: Foundations of infinitesimal calculus. Boston: Prindle, Weber & Schmidt 1976

    Google Scholar 

  8. Lang, S.: Algebra. Reading, Mass.: Addison-Wesley 1965

    Google Scholar 

  9. Robinson, A.: Metamathematical problems. J. Symbolic Logic38, 500–516 (1973)

    Google Scholar 

  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 1979

  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 1975

    Google Scholar 

  12. Schmidt, K.: Modelltheoretische Methoden in der Algebraischen Geometrie. Diplomarbeit, Kiel 1979

  13. Seidenberg, A.: Constructions in algebra. Trans. AMS197, 273–313 (1974)

    Google Scholar 

  14. Seidenberg, A.: Construction of the integral closure of a finite integral domain. II. Proc. AMS52, 368–372 (1975)

    Google Scholar 

  15. Seidenberg, A.: Constructions in a polynomial ring over the ring of integers. American J. of Math.100, 685–703 (1978)

    Google Scholar 

  16. Stolzenberg, G.: Constructive Normalization of an Algebraic Variety. Bull. AMS74, 595–599 (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Stanford University, 943051, Stanford, CA, USA

    L. van den Dries

  2. Abteilung Logik, Philosophisches Seminar, Universität Kiel, D-2300, Kiel, Federal Republic of Germany

    K. Schmidt

Authors
  1. L. van den Dries
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

van den Dries, L., Schmidt, K. Bounds in the theory of polynomial rings over fields. A nonstandard approach. Invent Math 76, 77–91 (1984). https://doi.org/10.1007/BF01388493

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388493

Keywords

Search

Navigation