On the Semigroup of Bi-Ideals of an Ordered Semigroup

Abstract

The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.