Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 1
Abstract
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. Keywords: quasi k-ideal, strong quasi k-ideal, strong quasi k-simple, t-ksimple, t-k-Archimedean. 2010 Mathematics Subject Classification: 16Y60.
Authors and Affiliations
Kanchan Jana, Anjan Bhuniya
Keywords
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