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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access May 31, 2016

Semigroup of k-bi-Ideals of a Semiring with Semilattice Additive Reduct

A. K. Bhuniya and K. Jana
From the journal Demonstratio Mathematica

Abstract

We associate a semigroup B(S) to every semiring S with semilattice additive reduct, namely the semigroup of all k-bi-ideals of S; and such semirings S have been characterized by this associated semigroup B(S). A semiring S is k-regular if and only if B(S) is a regular semigroup. For the left k-Clifford semirings S, B(S) is a left normal band; and consequently, B(S) is a semilattice if S is a k-Clifford semiring. Also we show that the set Bm(S) of all minimal k-bi-ideals of S forms a rectangular band and Bm(S) is a bi-ideal of the semigroup B(S).

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Received: 2014-4-8
Revised: 2014-6-13
Published Online: 2016-5-31
Published in Print: 2016-6-1

© by A. K. Bhuniya

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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