Distributive Lattices of λ-simple Semirings
T. Mondal · Iranian Journal of Mathematical Sciences and Informatics · 2022
In this paper, we study the decomposition of semirings with a semilattice additive reduct.For, we introduce the notion of principal left k-radicals Λ(a) = {x ∈ S | a l -→ ∞ x} induced by the transitive closure l -→ ∞ of the relation l -→ which induce the equivalence relation λ.Again non-transitivity of l -→ yields an expanding family { l -→ n } of binary relations which associate subsets Λn(a) for all a ∈ S, which again induces an equivalence relation λn.We also define λ(λn)-simple semirings, and characterize the semirings which are distributive lattices of λ(λn)-simple semirings.