Semirings Which Are Distributive Lattices of κ-Simple Semirings

摘要

Here we characterize the semirings in SL+ that are distributive lattices of k-simple(left k-simple) semirings. A semiring is a distributive lattice of k-simple(left k- simple) semirings if and only if every κ-ideal(left k-ideal) is a semiprime k-ideal. Also a semiring for which every κideal(left k-ideal) is completely prime is a chain of k-simple(left k-simple) semirings.