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...
| Autores: | , |
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| 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 |
| 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. |
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