Geodesic
Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 27-43.

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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.
Keywords: quasi k-ideal, strong quasi k-ideal, strong quasi k-simple, t-k-simple, t-k-Archimedean 
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Bhuniya, Anjan; Jana, Kanchan. Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 27-43. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a1/

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