Communications of the
Korean Mathematical Society CKMS

In this paper we introduce and give some characterizations of $(m,n)$-regular $le$-$\Gamma$-semigroup in terms of $(m,n)$-ideal elements and $(m,n)$-quasi-ideal elements. Also, we give some characterizations of subid-empotent $(m,n)$-ideal elements in terms of $r_{\alpha}$- and $l_{\alpha}$- closed elements.

Keywords: $\Gamma$-semigroup, $po$-$\Gamma$-semigroup, $poe$-$\Gamma$-semigroup, $\vee e$-$\Gamma$-semigroup, $le$-$\Gamma$-semigroup, $(m,n)$-ideal element, $(m,n)$-regular $le$-$\Gamma$-semigroup, $(m,n)$-quasi-ideal element, bi-ideal elements

MSC numbers: 06F99, 06F05, 20M10