Geodesic
Regularity of Semigroups in Terms of Hybrid Ideals and Hybrid Bi-Ideals
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 6, p. 857

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

In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals and hybrid bi-ideals. We also characterize the left and right simple and the completely regular semigroups utilizing hybrid ideals and hybrid bi-ideals. We show that a semigroup $\mathcal{S}$ is left simple if and only if it is hybrid left simple. We also prove that if a semigroup $\mathcal{S}$ is intra-regular, then for each hybrid ideal $\tilde{j}_µ$ of $\mathcal{S},$ we have $\tilde{j}_µ(r_1r_2)=\tilde{j}_µ(r_2r_1)$ for all $r_1,r_2\in \mathcal{S}$.
Classification : 20M12, 20M17, 06D72
Keywords: Semigroup, ideals, regular, hybrid structure, hybrid ideal, hybrid bi-ideal and hybrid product 
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     author = {Balasubramanian Elavarasan and Young Bae Jun},
     title = {Regularity of {Semigroups} in {Terms} of {Hybrid} {Ideals} and {Hybrid} {Bi-Ideals}},
     journal = {Kragujevac Journal of Mathematics},
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Balasubramanian Elavarasan; Young Bae Jun. Regularity of Semigroups in Terms of Hybrid Ideals and Hybrid Bi-Ideals. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 6, p. 857 . http://geodesic.mathdoc.fr/item/KJM_2022_46_6_a1/