Topological Characterization of Certain Classes of Almost Distributive Lattices

Topological characterization of Gelfand and zero dimensinal semirings

“…In [1], Al-Ezeh endowed Spec(L), where L is a distributive lattice with 0 and 1, with two topologies, the τ z -topology and the D-topology, and he proved that this two topologies coincide on Spec(L) and M ax(L) iff L is a boolean and normal lattice, respectively. In [3], Rafi and Rao introduced the concept of D-topology on Spec(R), where R is a almost distributive lattice (ADL), and characterized those ADLs for which topologies coincide on Spec(R) and M in(R). In this paper, the concept of D-topology is introduced on Spec(R), where R is a semiring, we do a similar study, as a consequence, we obtain a result given in [1] for distributive lattices.…”