Resumen de Topological characterization of Gelfand and zero dimensinal semirings

Jorge Vielma, Luz Marchan

• Let R be a conmutative semiring with 0 and 1, and let Spec(R) be the set of all proper prime ideals of R. Spec(R) can be endowed with two topologies, the Zariski topology and the D-topology.  Let Max R denote the set of all maximals  prime ideals of R. We prove that the two topologies coincide on Spec(R) and on Max R if and only if R is zero dimensional and Gelfand semiring, respectively.