Topological characterization of Gelfand and zero dimensinal semirings

• Autores: Jorge Vielma, Luz Marchan
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 19, Nº. 2, 2018, págs. 217-222
• Idioma: inglés
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• Resumen

  • 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.