On the Semigroup of Bi-Ideals of an Ordered Semigroup
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Authors: S. MALLICK AND K. HANSDA
DOI: 10.46793/KgJMat2303.339M
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 ???? of bands, we characterize the ordered semigroup S such that ℬ(S) ∈????.
Keywords:
Bi-ideal, regular, Clifford, left Clifford, locally testable, left normal band, normal band, rectangular band.
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