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December 2015 Semirings which are distributive lattices of $t$-$k$-simple semirings
Tapas Kumar Mondal, Anjan Kumar Bhuniya
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Tbilisi Math. J. 8(2): 149-157 (December 2015). DOI: 10.1515/tmj-2015-0018

Abstract

A semiring $S$ is said to be a $t$-$k$-simple semiring if it has no non-trivial proper left $k$-ideal and no non-trivial proper right $k$-ideal. We introduce the notion of $t$-$k$-simple semirings and characterize the semirings in $\mathbb{SL^{+}}$, the variety of all semirings with a semilattice additive reduct, which are distributive lattices of $t$-$k$-simple subsemirings. A semiring $S$ is a distributive lattice of $t$-$k$-simple subsemirings if and only if every $k$-bi-ideal in $S$ is completely semiprime $k$-ideal. Also the semirings for which every $k$-bi-ideal is completely prime has been characterized.

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Tapas Kumar Mondal. Anjan Kumar Bhuniya. "Semirings which are distributive lattices of $t$-$k$-simple semirings." Tbilisi Math. J. 8 (2) 149 - 157, December 2015. https://doi.org/10.1515/tmj-2015-0018

Information

Received: 11 November 2014; Accepted: 30 June 2015; Published: December 2015
First available in Project Euclid: 12 June 2018

zbMATH: 1321.16035
MathSciNet: MR3383790
Digital Object Identifier: 10.1515/tmj-2015-0018

Subjects:
Primary: 16Y60

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 2 • December 2015
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