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

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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 
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/
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     title = {Regularity of {Semigroups} in {Terms} of {Hybrid} {Ideals} and {Hybrid} {Bi-Ideals}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {857 },
     year = {2022},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_6_a1/}
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