Skip to main content
SpringerLink
Log in

Group ideals in a semigroup of measures

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

In this paper we introduce the notion of a group ideal in a semigroup. We shall prove that all group ideals of a compact affine semigroup are convex and dense. This generalizes many results in the literature concerning ideals in semigroups.

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. Chow, H. L., On supports of semigroups of measures, Proc. Edinburgh Math. Soc. 19 (2) (1974), 31–33.

    Google Scholar 

  2. —, Prime ideals in a semigroup of measures, Colloquium Math. 35 (1975), 109–111.

    Google Scholar 

  3. —, Radicals and semiprime ideals, Acta Math. Acad. Sci. Hung. 29 (1–2) (1977), 49–50.

    Google Scholar 

  4. —, Nilpotent measures on compact semigroups, Bull. Austr. Math. Soc. 12 (1975), 149–153.

    Google Scholar 

  5. —, Quasi-nilpotent sets in semigroups, Proc. Amer. Math. Soc. 52 (1975), 393–397.

    Google Scholar 

  6. —, On compact affine semigroups, Semigroup Forum 11 (1975), 146–152.

    Google Scholar 

  7. —, On bonds in semigroups of measures, Nata Math. 9 (2) (1976), 89–91.

    Google Scholar 

  8. —, Maximal ideals in a semigroup of measures, Czech. Math. J. 26 (1976), 270–272.

    Google Scholar 

  9. Chow, H. L., Remarks on maximal left ideals of semigroups, Monatshefte für Math. (1976), 257–260.

  10. Chow, H. L., Probability measures on locally compact semigroups, Math. Balkanica 6 (1976), 33–36.

    Google Scholar 

  11. Cohen, H. and H. S. Collins, Affine semigroups, Trans. Amer. Math. Soc. 93 (1959), 97–113.

    Google Scholar 

  12. Collins, H. S., Remarks on affine semigroups, Pacific Journal of Mathematics 12 (1962), 449–455.

    Google Scholar 

  13. Glicksberg, I., Convolution semigroups of measures, Pacific Journal of Mathematics 9 (1959), 51–67.

    Google Scholar 

  14. Mukherjea, A. and N. A. Tserpes, Measures on Topological Semigroups, Lecture Notes in Mathematics 547 (1976), Springer-Verlag, New York.

    Google Scholar 

  15. Numakura, K., Prime ideals and idempotents in compact semigroups, Duke Math. J. 24 (1957), 671–679.

    Google Scholar 

  16. Paalman-de Miranda, Topological Semigroups, Mathematisch Centrum, Amsterdam, 2nd edition (1970).

  17. Pym, J., Idempotent probability measures on compact semitopological semigroups, Proc. Amer. Math. Soc. 21 (1969), 499–501.

    Google Scholar 

  18. Shum, K.-P., On the boundary of algebraic radicals in topological semigroups, Acta Math. Acad. Sci. Hung. 25 (1974), 15–19.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong

    Kar-Ping Shum

Authors
  1. Kar-Ping Shum
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Michael Mislove

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shum, KP. Group ideals in a semigroup of measures. Semigroup Forum 22, 325–329 (1981). https://doi.org/10.1007/BF02572811

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02572811

Keywords

Search

Navigation