Distributive Lattices of Jacobson Rings


Yong Shao, Siniša Crvenković, Melanija Mitrović




We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.