Geodesic
On the Semigroup of Bi-Ideals of an Ordered Semigroup
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 339 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The purpose of this paper is to characterize an ordered semigroup $S$ in terms of the properties of the associated semigroup $\mathcal{B}(S)$ of all bi-ideals of $S$. We show that an ordered semigroup $S$ is a Clifford ordered semigroup if and only if $\mathcal{B}(S)$ is a semilattice. The semigroup $\mathcal{B}(S)$ is a normal band if and only if the ordered semigroup $S$ is both regular and intra regular. For each subvariety $\mathcal{V}$ of bands, we characterize the ordered semigroup $S$ such that $\mathcal{B}(S)\in \mathcal{V}$.
Classification : 20M10 06F05
Keywords: Bi-ideal, regular, Clifford, left Clifford, locally testable, left normal band, normal band, rectangular band 
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     title = {On the {Semigroup} of {Bi-Ideals} of an {Ordered} {Semigroup}},
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Susmita Mallick; Kalyan Hansda. On the Semigroup of Bi-Ideals of an Ordered Semigroup. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 339 . http://geodesic.mathdoc.fr/item/KJM_2023_47_3_a0/