Topological characterization of gelfand and zero dimensional semiring

Abstract:

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 MaxR denote the set of all maximal prime ideals of R. We prove that the two topologies coincide on Spec(R) and on MaxR if and only if R is zero dimensional and Gelfand semiring, respectively.

Año de publicación:

2018

Keywords:

• D-topology
• Zariski topology
• Conmutative semiring
• Gelfand semiring
• Zero dimensional semiring

Fuente:

scopus

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