Gamma-semigroups with Unities and Morita Equivalence for Monoids

Authors

  • Sujit Kumar Sardar Department of Mathematics Jadavpur University. Jadavpur, Kolkata. India
  • Sugata Gupta Department of Mathematics, Jadavpur University, Jadavpur. Kolkata-700032 INDIA
  • Kar Ping Shum Institute of Mathematics, Yunnan University, China

Keywords:

$\Gamma$-semigroup, Morita equivalence for monoids, Morita invariant.

Abstract

In this paper we show that the left operator and right operator semi groups of a Γ-semigroup with unities are Morita equivalent monoids. It is also deduced that if L and R are two Morita equivalent monoids then a Γ-semigroup with unities can be constructed such that its left and right operator monoids are isomorphic to L and R respectively. This result is used to obtain some properties of monoids which remain invariant under Morita equivalence. 

Author Biographies

  • Sujit Kumar Sardar, Department of Mathematics Jadavpur University. Jadavpur, Kolkata. India

    Associate Professor,

    Department of Mathematics,

    Jadvpur University.

    Jadavpur. Kolkata-700032.

  • Sugata Gupta, Department of Mathematics, Jadavpur University, Jadavpur. Kolkata-700032 INDIA

    UGC, India Junior Research Fellow

    Department of Mathematics,
    Jadavpur University, Jadavpur.
    Kolkata-700032
    INDIA

  • Kar Ping Shum, Institute of Mathematics, Yunnan University, China

    Professor,

    Institute of Mathematics,

    Yunnan University, China

Downloads

Published

2013-01-23

Issue

Vol. 6 No. 1: (January 2013)

Section

Algebra

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Gamma-semigroups with Unities and Morita Equivalence for Monoids. (2013). European Journal of Pure and Applied Mathematics, 6(1), 1-10. https://www.ejpam.com/index.php/ejpam/article/view/1726