SpringerLink
Log in

The least regular order with respect to a regular congruence on ordered Γ-semigroups

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the Γ-semigroups. We can see that any semigroup can be considered as a Γ-semigroup. In this paper, we introduce and characterize the concept of the regular congruences on ordered Γ-semigroups and prove the following statements on an ordered Γ-semigroup M:

  1. (1)

    Every ordered semilattice congruences is a regular congruence.

  2. (2)

    There exists the least regular order on the Γ-semigroup M/ρ with respect to a regular congruence ρ on M.

  3. (3)

    The regular congruences are not ordered semilattice congruences in general.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. **e, X. Y., Wu, M. F.: On congruences on ordered semigroups. Mathematica Japonica, 45, 81–84 (1997)

    MathSciNet  MATH  Google Scholar 

  2. Dutta, T. K., Adhikari, N. C.: On partially ordered Γ-semigroups. Southeast Asian Bull. Math., 28, 1021–1028 (2004)

    MathSciNet  MATH  Google Scholar 

  3. **e, X. Y.: Remarks on regular congruences on po-semigroups. Southeast Asian Bull. Math., 24, 661–666 (2000)

    MathSciNet  MATH  Google Scholar 

  4. Siripitukdet, M., Iampan, A.: On the least (ordered) semilattice congruences in ordered Γ-semigroups. Thai J. Math., 4, 403–415 (2006)

    MathSciNet  MATH  Google Scholar 

  5. Iampan, A., Siripitukdet, M.: On minimal and maximal ordered left ideals in po-Γ-semigroups. Thai J. Math., 2, 275–282 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Sen, M. K., Saha, N. K.: Orthodox Γ-semigroups. Int. J. Math. Math. Sci., 13, 527–534 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sen, M. K.: On Γ-semigroups. Proceedings of the International Conference on Algebra and It’s Applications, Decker Publication, New York, 1981, p. 301

    Google Scholar 

  8. Sen, M. K., Saha, N. K.: On Γ-semigroup I. Bull. Calcutta Math. Soc., 78, 180–186 (1986)

    MathSciNet  MATH  Google Scholar 

  9. Saha, N. K.: On Γ-semigroup II. Bull. Calcutta Math. Soc., 79, 331–335 (1987)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Manoj Siripitukdet & Aiyared Iampan

Authors
  1. Manoj Siripitukdet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aiyared Iampan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manoj Siripitukdet.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Siripitukdet, M., Iampan, A. The least regular order with respect to a regular congruence on ordered Γ-semigroups. Acta. Math. Sin.-English Ser. 28, 975–982 (2012). https://doi.org/10.1007/s10114-011-9702-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-011-9702-x

Keywords

MR(2000) Subject Classification

Search

Navigation