Further studies on ordered (*, Γ)-semigroups

Abstract

In this paper, we study the *-filters of ordered (*,Γ)-seniigroups in detail. To begin with, we introduce the concept of *-filters of an ordered (*, Γ)semigroup, and investigate some related properties. Furthermore, we construct a complete semilattice congruence M on an ordered (*, Γ)-semigroup M in terms of the principal *-filter and give some characterizations of intra-regular ordered (*, Γ)-semigroups. Finally, we obtain some properties of the complete semilattice congruence classes of an ordered (*, Γ)-semigroup M. In addition, for any a ∈ M, the relationship between the congruence class (a)_N- and the principal *-filter N(a) generated by a is also established. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.