Geodesic
On the Semigroup of Bi-Ideals of an Ordered Semigroup
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 339

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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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/