k-spaces of non-domain-valued geometric points
[EN] The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a k-algebra and this new k-space becomes a generalization of the corresponding Zariski space. We prove that a k-space is T0, quasi-comp...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| 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:10251/210149 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/210149 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometric point Connectedness Spectral space |
| Sumario: | [EN] The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a k-algebra and this new k-space becomes a generalization of the corresponding Zariski space. We prove that a k-space is T0, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such k-spaces. We conclude with a question about the construction of a sheaf of k-spaces similar to affine schemes. |
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