On ordered $\Gamma$-semigroups ($\Gamma$-semigroups)

Abstract

We add here some further characterizations to the characterizations of strongly regular ordered $\Gamma$-semigroups already considered in Hacettepe J. Math. 42 (2013), 559--567. Our results generalize the characterizations of strongly regular ordered semigroups given in the Theorem in Math. Japon. 48 (1998), 213--215, in case of ordered $\Gamma$-semigroups. The aim of writing this paper is not just to add a publication in $\Gamma$-semigroups but, mainly, as a continuation of the paper "On regular duo $po$-$\Gamma$-semigroups in Math. Slovaca 61 (2011), 871--884, to publish a paper which serves as an example to show what a $\Gamma$-semigroup is and give the right information about this structure.