Skip to main content
SpringerLink
Log in

An application of \(\Gamma \)-semigroups techniques to the Green’s Theorem

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

The concept of a \(\Gamma \)-semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green’s relations play an essential role in studying the structure of semigroups. In the present paper we deal with an application of \(\Gamma \)-semigroups techniques to the Green’s Theorem in an attempt to show the way we pass from semigroups to \(\Gamma \)-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. Barnes, W.E.: On the \(\Gamma \)-rings of Nobusawa. Pacif. J. Math. 18, 411–422 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chinram, R., Siammai, P.: Green’s lemma and Green’s theorem for \(\Gamma \)-semigroups. Lobachevskii J. Math. 30(3), 208–213 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups, vol. I. Mathematical Surveys, No. 7 American Mathematical Society, Providence, R.I. (1961)

  4. Dutta, T.K., Chatterjee, T.K.: Green’s equivalences on \(\Gamma \)-semigroup. Bull. Calcutta Math. Soc. 80(1), 30–35 (1988)

    MathSciNet  MATH  Google Scholar 

  5. Kehayopulu, N.: On prime, weakly prime ideals in \(po\)-\(\Gamma \)-semigroups. Lobachevskii J. Math. 30(4), 257–262 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Luh, Jiang: On the theory of simple \(\Gamma \)-rings. Mich. Math. J. 16, 65–75 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  7. Nobusawa, N.: On a generalization of the ring theory. Osaka J. Math. 1, 81–89 (1964)

    MathSciNet  MATH  Google Scholar 

  8. Saha, N.K.: The maximum idempotent separating congruence on an inverse \(\Gamma \)-semigroup. Kyungpook Math. J. 34(1), 59–66 (1994)

    MathSciNet  MATH  Google Scholar 

  9. Sen, M.K.: On \(\Gamma \)-semigroup. In: Algebra and its Applications, Int. Symp. New Delhi, 1981. Lecture Notes in Pure and Appl. Math. vol. 91, pp. 301–308. Dekker, New York (1984)

  10. Sen, M.K., Saha, N.K.: On \(\Gamma \)-semigroup. I. Bull. Calcutta Math. Soc. 78(3), 180–186 (1986)

    MATH  Google Scholar 

  11. Sen, M.K., Saha, N.K.: The maximum idempotent-separating congruence on an orthodox \(\Gamma \)-semigroup. J. Pure Math. 7, 39–47 (1990)

    MathSciNet  MATH  Google Scholar 

  12. Sen, M.K., Saha, N.K.: Orthodox \(\Gamma \)-semigroups. Int. J. Math. Math. Sci. 13(3), 527–534 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sen, M.K., Seth, A.: Radical of \(\Gamma \)-semigroup. Bull. Calcutta Math. Soc. 80(3), 189–196 (1988)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimiopolis, 15784, Athens, Greece

    Niovi Kehayopulu

Authors
  1. Niovi Kehayopulu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Niovi Kehayopulu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kehayopulu, N. An application of \(\Gamma \)-semigroups techniques to the Green’s Theorem. Afr. Mat. 29, 65–71 (2018). https://doi.org/10.1007/s13370-017-0526-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-017-0526-4

Keywords

Mathematics Subject Classification

Search

Navigation