ON INT-SOFT quasi-$\Gamma$-IDEALS OF AN ORDERED $\Gamma$-SEMIGROUP

Abstract

In this paper, we introduce the concept of
int-soft $\Gamma$-semigroup, int-soft quasi-$\Gamma$-semigroup and int-soft
left (resp., right) $\Gamma$-semigroup of ordered $\Gamma$-semigroup over an
initial universal set $U$. We investigate some properties of int-soft
quasi-$\Gamma$-ideals and left (resp., right) $\Gamma$-ideals of ordered
$\Gamma$-semigroup. Moreover, we define critical soft point of ordered
$\Gamma$-semigroup. By using the notion of critical soft point, we define
semiprime int-soft quasi-$\Gamma$-ideals of ordered $\Gamma$-semigroups. We
characterize completely regular ordered $\Gamma$-semigroups in terms of their
int-soft quasi-$\Gamma$-ideals and semiprime int-soft quasi-$\Gamma$-ideals.
Furthermore, we define semilattice of left and right simple sub-$\Gamma$-semigroups of
ordered $\Gamma$-semigroups and characterize semilattice of left and right
simple sub-$\Gamma$-semigroups in terms of their int-soft quasi-$\Gamma$-ideal.