Algebra universalis

, 79:6 | Cite as

Representation of normal bands as semigroups of k-bi-ideals of a semiring

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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.

Keywords

k-ideal k-bi-ideal k-regular semiring Intra k-regular semiring Normal band 

Mathematics Subject Classification

Primary 16Y60 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsVisva-BharatiSantiniketanIndia
  2. 2.Department of MathematicsKatwa CollegeKatwaIndia

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