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

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Bhuniya A., Jana K.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 1

27-43

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.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Bhuniya A.

1 Jana K.

1 2014

Wyniki wyszukiwania

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