Some results on the intermediate rings of complex-valued continuous functions
[EN] Let X be a Tychonoff space and C(X), C ( X , ℂ ) be the rings of all real-valued and complex-valued continuous functions defined on X respectively. For each intermediate subring A(X) of C(X), Acharyya and De have introduced the notion of zβA -ideals in A(X) and zβA-filters on β X. For each A(X)...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/227678 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/227678 |
| Access Level: | acceso abierto |
| Palavra-chave: | Ring of complex-valued continuous functions Z-ideals Absolutely convex ideals zβ[A(X)]c-ideals Hull-kernel topology Structure space |
| Resumo: | [EN] Let X be a Tychonoff space and C(X), C ( X , ℂ ) be the rings of all real-valued and complex-valued continuous functions defined on X respectively. For each intermediate subring A(X) of C(X), Acharyya and De have introduced the notion of zβA -ideals in A(X) and zβA-filters on β X. For each A(X), we extend this notion to zβ[A(X)]c -ideals and zβ[A(X)]c-filters for an intermediate subring [A(X)]c of C ( X , ℂ ). We establish a correspondence between the collection of zβ[A(X)]c-ideals in the subrings [A(X)]c of C ( X , ℂ ) and the collection of zβ[A(X)]c-filters on β X. We study the properties of the zβ[A(X)]c-ideals. We also deduce that the structure space of the subrings [A(X)]c is homeomorphic to β X. |
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