On m-quasi-ideals in m-regular ordered semigroups

Abstract

In this paper we characterize left(right) ideals, bi-ideals and quasi-ideals of an ordered semigroup by an index $m$ and give some important interplays between these ideals. The concept of m-regularity of an ordered semigroups has been introduced. Moreover m-regular ordered semigroups are characterized by their m-quasi-ideals and the fact that for any m-regular ordered semigroups $A$, the set $Q_A$ of all m-quasi-ideals of $A$, with multiplication defined by: $Q_1\circ Q_2=(Q_1{Q}_2]$, for all $Q_1,Q_2\in Q_A$, is a m-regular semigroup is obtained here.