Topological characterization of Gelfand and zero dimensional semirings

Jorge Vielma; Luz Marchan

doi:10.4995/agt.2018.7952

Authors

Jorge Vielma Escuela Superior Politécnica del Litoral (ESPOL)
Luz Marchan Escuela Superior Politécnica del Litoral (ESPOL)

DOI:

https://doi.org/10.4995/agt.2018.7952

Keywords:

Zariski topology, D-topology, conmutative semiring, Gelfand semiring, 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 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.

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Author Biographies

Jorge Vielma, Escuela Superior Politécnica del Litoral (ESPOL)

Facultad de Ciencias Naturales y Matemáticas

Luz Marchan, Escuela Superior Politécnica del Litoral (ESPOL)

Facultad de Ciencias Naturales y Matemáticas

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