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Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct

Anjan Kumar Bhuniya;  Kanchan Jana — 2014

Discussiones Mathematicae - General Algebra and Applications

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...

Bi-ideals in k-regular and intra k-regular semirings

Anjan K. Bhuniya;  Kanchan Jana — 2011

Discussiones Mathematicae - General Algebra and Applications

Here we introduce the k-bi-ideals in semirings and the intra k-regular semirings. An intra k-regular semiring S is a semiring whose additive reduct is a semilattice and for each a ∈ S there exists x ∈ S such that a + xa²x = xa²x. Also it is a semiring in which every k-ideal is semiprime. Our aim in this article is to characterize both the k-regular semirings and intra k-regular semirings using of k-bi-ideals.

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