Regularity of Semigroups in Terms of Hybrid Ideals and Hybrid Bi-Ideals
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Authors: B. ELAVARASAN AND Y. B. JUN
DOI: 10.46793/KgJMat2206.857E
Abstract:
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 ???? is left simple if and only if it is hybrid left simple. We also prove that if a semigroup ???? is intra-regular, then for each hybrid ideal
μ of ????, we have 
μ(r1r2) = 
μ(r2r1) for all
r1,r2 ∈????.
Keywords:
Semigroup, ideals, regular, hybrid structure, hybrid ideal, hybrid bi-ideal and hybrid product.
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