Skip to main content
Log in

On ring derivations and quadratic functionals

  • Research Papers
  • Published:
aequationes mathematicae Aims and scope Submit manuscript

Summary

In this note the general form of ring derivations on a function algebra is obtained. In particular, we give a very simple proof of the following result of Nandakumar: a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set. Using this theorem we prove a result concerning representability of quadratic functionals by bilinear forms.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Browder, A.,Introduction to function algebras, Benjamin, New York, 1969.

    Google Scholar 

  2. Cartier, P.,Derivations dans les corps, Séminaire E.N.S.-Géometrique algébrique, Paris,8 (1955/56).

  3. Davison, T. M. K.,Jordan derivations and quasi-bilinear forms, Comm. Algebra12 (1) (1984), 23–32.

    Google Scholar 

  4. Gleason, A. M.,The definition of a quadratic form, Amer. Math. Monthly73 (1966), 1049–1056.

    Google Scholar 

  5. Johnson, B. E. andSinclair, A. M.,Continuity of derivations and a problem of Kaplansky, Amer. J. Math.90 (1968), 1067–1073.

    Google Scholar 

  6. Kurepa, S.,The Cauchy functional equation and scalar product in vector spaces, Glasnik Mat.-Fiz. Astr.19 (1964), 23–36.

    Google Scholar 

  7. Nandakumar, N. R.,Ring derivations on function algebras, Canad. Math. Bull.33 (1) (1990), 69–72.

    Google Scholar 

  8. Singer, I. M. andWermer, J.,Derivations on commutative algebras, Math. Ann.129 (1955), 260–264.

    Article  Google Scholar 

  9. Vukman, J.,Some remarks on derivations in Banach algebras and related results, Aequationes Math.36 (1988), 165–175.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported by the Research Council of Slovenia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

šemrl, P. On ring derivations and quadratic functionals. Aeq. Math. 42, 80–84 (1991). https://doi.org/10.1007/BF01818480

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01818480

AMS (1980) subject classification

Navigation