Skip to main content
SpringerLink
Log in

The class number of hereditary orders in non-Eichler algebras over global function fields

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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. Denert, M.: Orders in non-Eichler(R)-algebras over global function fields, having the cancellation property. Scand. J. Math. (to appear)

  2. Denert, M.: Affine and projective orders in central simple algebras over global function fields. (An analytic approach to the ideal theory.) Ph-D Thesis Gheat, 1987

  3. Denert, M., Van Geel, J.: Cancellation property for orders in non Eichler division algebras over global function fields. J. Reine Angew. Math.368, 165–171 (1986)

    Google Scholar 

  4. Denert, M., Van Geel, J.: Orders in quaternion algebras over global function fields, having the cancellation property. Preprint, J. Number Theory (to appear)

  5. Eichler, M.: Über die Idealklassenzahl total definlter Quaternionen-Algebren. Math. Z.43, 102–109 (1937)

    Google Scholar 

  6. Eichler, M.: Zur Zahlentheorie der Quaternionen-Algebren. J. Reine Angew. Math.195, 127–151 (1955)

    Google Scholar 

  7. Fröhlich, A.: Locally free modules over arithmetic orders. J. Reine Angew. Math.274/275, 112–138 (1975)

    Google Scholar 

  8. Fröhlich, A., Reiner, I., Ullom, S.: Class groups and Picard groups of orders. Proc. Lond. Math. Soc.29, 405–434 (1974)

    Google Scholar 

  9. Noether, E.: Zerfallende verschrankte Produkte und ihre Maximal-Ordarungen. Actualités Sientif. indus.148, 5–15 (1934)

    Google Scholar 

  10. Pizer, A.: Type numbers of Eichler orders. J. Reine Angew. Math.264, 76–102 (1973)

    Google Scholar 

  11. Reiner, I.: Maximal orders. New York: Academic Press 1975

    Google Scholar 

  12. Swan, R.: Strong approximation and locally free modules. In: Ring theory and algebra. III. B. McDonald (ed.). New York 1980

  13. Vigneras, M.F.: Simplification pour les ordres des corps de quaternions totalement définis. J. Reine Angew. Math.286/287, 257–277 (1975)

    Google Scholar 

  14. Vigneras, M.F.: Arithmétique des algèbres de quaternions. Lecture Notes Mathematics, Vol. 800. Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  15. Van Deuren, J.P., Van Geel, J., Van Ostaeyen, F.: Genus and a Riemann-Roch theorem for non-commutative function fields in one variable. Séminaire d'Algèbre Paul Dubreil et M.P. Malliavin, Proc. Paris 1980. Lecture Notes Mathematics, Vol. 867, pp. 295–318. Berlin Heidelberg New York: Springer 1981

    Google Scholar 

  16. Weil, A.: Adeles and algebraic groups. I.A.S., Princeton 1961

Download references

Author information

Authors and Affiliations

  1. Seminar of Algebra, State University of Ghent, Galglaan 2, B-9000, Ghent, Belgium

    Marleen Denert & Jan Van Geel

Authors
  1. Marleen Denert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Van Geel
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first author is supported by an N.F.W.O.-grant

Rights and permissions

Reprints and permissions

About this article

Cite this article

Denert, M., Van Geel, J. The class number of hereditary orders in non-Eichler algebras over global function fields. Math. Ann. 282, 379–393 (1988). https://doi.org/10.1007/BF01460041

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01460041

Keywords

Search

Navigation