Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1213,
author = {Anjan Kumar Bhuniya and Kanchan Jana},
title = {Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {34},
year = {2014},
pages = {27-43},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1213}
}
Anjan Kumar Bhuniya; Kanchan Jana. Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct. Discussiones Mathematicae - General Algebra and Applications, Tome 34 (2014) pp. 27-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1213/
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