Skip to main content

The divisor class groups of some rings of global real analytic, Nash or rational regular functions

Contributions Des Participants

Part of the Lecture Notes in Mathematics book series (LNM,volume 959)

Keywords

  • Vector Bundle
  • Fractional Ideal
  • Zariski Open Subset
  • Algebraic Subset
  • Trivial Vector Bundle

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benedetti, R., Tognoli A.: Approximation theorems in real algebraic geometry, Seminaire Risler, Université Paris VII, 1980.

    Google Scholar 

  2. Benedetti R., Tognoli A.: On real algebraic vector bundles, Bull.Sc. Math., 104, 89–112, (1980).

    MathSciNet  MATH  Google Scholar 

  3. Bochnak J.: Un critère de factorialité des anneaux globaux réguliers, C.R.A.S. Paris, 283, 285–286, (1976).

    MathSciNet  MATH  Google Scholar 

  4. Bochnak J.: Sur la factorialité des anneaux de fonctions analytiques. C.R.A.S. Paris, 283, 269–273, (1974).

    MathSciNet  MATH  Google Scholar 

  5. Bochnak J., Efroymson G.: Real Algebraic Geometry and the 17th Hilbert Problem, Math. Ann. 251, 213–241 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Borel A., Haefliger A.: La class d’homologie fondamentale d’un espace analytique, Bull.Soc.Math. France 89, 461–513, (1961).

    MathSciNet  MATH  Google Scholar 

  7. Bourbaki N.: Algèbre Commutative, Ch. VII, Paris 1965.

    Google Scholar 

  8. Efroymson G.: Nash rings on planar domains, Trans.Amer.Math.Soc. 249(2), 435–445, (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Fossum R.: The Divisor Class Group of a Krull Domain, Springer Verlag 1973.

    Google Scholar 

  10. Hironaka H.: Introduction to real analytic sets and real analytic maps, Instituto Matematico “L. Tonelli” dell’Universita di Pisa 1973.

    Google Scholar 

  11. Hironaka H.: Subanalytic sets, Volume in honor of Y.Akizuki, Number theory, algebraic geometry and commutative algebra, 453–493, Tokyo 1973.

    Google Scholar 

  12. Hirzebruch F.: Topological methods in Algebraic Geometry, Springer Verlag, 1966.

    Google Scholar 

  13. Hubbard J.: On the cohomology of Nash sheaves. Topology 11, 265–270. (1974).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Kucharz W.: On analytic sets with given singularities, to appear.

    Google Scholar 

  15. Palais R.: Equivariant, real algebraic differential topology, Brandeis University, (preprint), 1972.

    Google Scholar 

  16. Risler J.J.: Sur l’anneau des fonctions de Nash globales, Ann.Sc. de l’Ecole Nor.Sup. 8 (3), 365–378, (1975).

    MathSciNet  MATH  Google Scholar 

  17. Samuel P.: Anneaux Factoriels, Bol.Soc.Math., Sâo Paulo, 1964.

    Google Scholar 

  18. Serre J.P.: Faisceaux algébriques cohérents, Ann. of Math., 81, 197–278, (1955).

    CrossRef  MATH  Google Scholar 

  19. Shiota M.: Sur la factorialité de l’anneau des fonctions analytiques, C.R.A.S. Paris 285, 253–255, (1977).

    MathSciNet  MATH  Google Scholar 

  20. Shiota M.: On the unique factoriality of the ring of Nash functions Publ. R.I.M.S., Kyoto University, to appear.

    Google Scholar 

  21. Shiota M.: Sur la factorialité de l’anneau des fonctions lisses rationnelles, C.R.A.S., Paris. 292, 67–70 (1981).

    MathSciNet  MATH  Google Scholar 

  22. Siu Y.: Noetheriannes of ring of holomorphic functions, Proc.Amer. Math. Soc. 21, (1969).

    Google Scholar 

  23. Silhol R.: Etude cohomologique des variètés algebriques réelles, preprint, University of Ferrara, (1980).

    Google Scholar 

  24. Tognoli A.: Algebraic approximation of manifolds and spaces. Seminaire Bourbaki, November 1979.

    Google Scholar 

  25. Tognoli A.: Une remarque sur les fibrés vectoriels analytiques et de Nash, C.R.A.S. Paris 290, 321–324 (1980).

    MathSciNet  MATH  Google Scholar 

  26. Tognoli A.: Algebraic geometry and Nash functions, Institutiones mathematicae, Vol. III, Acad. Press, London-New York, 1978.

    Google Scholar 

  27. Benedetti R., Tognoli A.: Remarks and counterexamples in real algebraic vector bundles and cycles, This volume.

    Google Scholar 

  28. Shiota M.: Real algebraic realization of characteristic classes, preprint, Kyoto University (1981).

    Google Scholar 

  29. Akbulut S., King H.: article in preparation, University of Maryland.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Bochnak, J., Kucharz, W., Shiota, M. (1982). The divisor class groups of some rings of global real analytic, Nash or rational regular functions. In: Colliot-Thélène, JL., Coste, M., Mahé, L., Roy, MF. (eds) Géométrie Algébrique Réelle et Formes Quadratiques. Lecture Notes in Mathematics, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062257

Download citation

  • DOI: https://doi.org/10.1007/BFb0062257

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11959-3

  • Online ISBN: 978-3-540-39548-5

  • eBook Packages: Springer Book Archive