Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
Anjan Kumar Bhuniya, Kanchan Jana · Discussiones Mathematicae - General Algebra and Applications · 2014
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(tk-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.