Topological characterization of Gelfand and zero dimensional semirings

[EN] 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...

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Detalles Bibliográficos
Autores: Vielma, Jorge, Marchan, Luz
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/109448
Acceso en línea:https://riunet.upv.es/handle/10251/109448
Access Level:acceso abierto
Palabra clave:Zariski topology
D-topology
Conmutative semiring
Gelfand semiring
Zero dimensional semiring
Descripción
Sumario:[EN] 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.