Representation of normal bands as semigroups of <Emphasis Type="Italic">k</Emphasis>-bi-ideals of a semiring |
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Authors: | Anjan Kumar Bhuniya Kanchan Jana |
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Institution: | 1.Department of Mathematics,Visva-Bharati,Santiniketan,India;2.Department of Mathematics,Katwa College,Katwa,India |
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Abstract: | Here we show that every normal band N can be embedded into the normal band \(\mathcal {B(S)}\) of all k-bi-ideals, the left part \(N/ \mathcal {R}\) of N into the left normal band \(\mathcal {R(S)}\) of all right k-ideals, the right part \(N/ \mathcal {L}\) of N into the right normal band \(\mathcal {L(S)}\) of all left k-ideals, and the greatest semilattice homomorphic image \(N/ \mathcal {J}\) of N into the semilattice of all k-ideals of a same k-regular and intra k-regular semiring S. |
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