Some topological aspects of ideals in quantales
[EN] As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain topological properties exhibited by distinguished classes of ideals. These ideals are equipped with quantale topolog...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| 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:10251/221873 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/221873 |
| Access Level: | acceso abierto |
| Palabra clave: | Quantale quasi-compactness sobriety spectral spaces |
| Sumario: | [EN] As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain topological properties exhibited by distinguished classes of ideals. These ideals are equipped with quantale topologies. The primary objectives encompass characterizing quantale spaces exhibiting sobriety, examining several conditions pertaining to quasi-compactness, and demonstrating that quantale spaces comprised of proper ideals adhere to the spectral properties as defined by Hochster. We introduce the notion of a strongly disconnected spaces and show that for a quantale with zero Jacobson radical, strongly disconnected quantale spaces containing all maximal ideals of the quantale imply existence of non-trivial idempotent elements in the quantale. Additionally, a sufficient criterion for establishing the connectedness of a quantale space is presented. Finally, we discuss on continuous maps between quantale spaces. |
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