Skip to main content
SpringerLink
Log in

Noncoherence of some rings of holomorphic functions in several variables as an easy consequence of the one-variable case

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

Using the facts that the disk algebra and the Wiener algebra are not coherent, we prove that the polydisc algebra, the ball algebra, and the Wiener algebra of the polydisc are not coherent.

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

Similar content being viewed by others

References

  1. Amar E.: Non cohérence de certains anneaux de fonctions holomorphes. Illinois Journal of Mathematics 25, 68–73 (1981)

    MathSciNet  MATH  Google Scholar 

  2. Glaz S.: Commutative coherent rings: historical perspective and current developments. Nieuw Archief voor Wiskunde 10(4), 37–56 (1992)

    MathSciNet  MATH  Google Scholar 

  3. Hickel M.: Non cohérence de certains anneaux de fonctions holomorphes. Illinois Journal of Mathematics 34, 515–525 (1990)

    MathSciNet  MATH  Google Scholar 

  4. Kaplansky I.: Commutative Rings. Allyn and Bacon, Boston, Mass (1970)

    MATH  Google Scholar 

  5. McVoy W.S., Rubel L.A.: Coherence of some rings of functions. Journal of Functional Analysis 21, 76–87 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mortini R., von Renteln M.: Ideals in the Wiener algebra W +. Journal of the Australian Mathematical Society Series A 46, 220–228 (1989)

    Article  MATH  Google Scholar 

  7. A. Quadrat, The fractional representation approach to synthesis problems: an algebraic analysis viewpoint. I. (Weakly) doubly coprime factorizations, SIAM Journal on Control Optimization 42 (2003), 266–299.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UMR 7502, Département de Mathématiques et InstitutÉlie Cartan de Lorraine, Université de Lorraine, Ile du Saulcy, 57045, Metz, France

    Raymond Mortini

  2. Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    Amol Sasane

Authors
  1. Raymond Mortini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amol Sasane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amol Sasane.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mortini, R., Sasane, A. Noncoherence of some rings of holomorphic functions in several variables as an easy consequence of the one-variable case. Arch. Math. 101, 525–529 (2013). https://doi.org/10.1007/s00013-013-0592-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-013-0592-2

Mathematics Subject Classification (1991)

Keywords

Search

Navigation