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)...

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Authors: Jamir, Yangersenba, Kharkamni, Longjaijai, Dutta, Sanghita
Format: article
Publication Date:2025
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/227678
Online Access:https://riunet.upv.es/handle/10251/227678
Access Level:Open access
Keyword:Ring of complex-valued continuous functions
Z-ideals
Absolutely convex ideals
zβ[A(X)]c-ideals
Hull-kernel topology
Structure space
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spelling Some results on the intermediate rings of complex-valued continuous functionsJamir, YangersenbaKharkamni, LongjaijaiDutta, SanghitaRing of complex-valued continuous functionsZ-idealsAbsolutely convex idealszβ[A(X)]c-idealsHull-kernel topologyStructure space[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.The second author would also like to thank the Council of Scientific and Industrial Research (CSIR) for financialsupport under CSIR-JRF scheme.Universitat Politècnica de ValènciaCouncil of Scientific and Industrial Research, IndiaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdftext/htmlhttps://riunet.upv.es/handle/10251/227678reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Compartir igual (by-nc-sa) http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2276782026-06-13T07:49:27Z
dc.title.none.fl_str_mv Some results on the intermediate rings of complex-valued continuous functions
title Some results on the intermediate rings of complex-valued continuous functions
spellingShingle Some results on the intermediate rings of complex-valued continuous functions
Jamir, Yangersenba
Ring of complex-valued continuous functions
Z-ideals
Absolutely convex ideals
zβ[A(X)]c-ideals
Hull-kernel topology
Structure space
title_short Some results on the intermediate rings of complex-valued continuous functions
title_full Some results on the intermediate rings of complex-valued continuous functions
title_fullStr Some results on the intermediate rings of complex-valued continuous functions
title_full_unstemmed Some results on the intermediate rings of complex-valued continuous functions
title_sort Some results on the intermediate rings of complex-valued continuous functions
dc.creator.none.fl_str_mv Jamir, Yangersenba
Kharkamni, Longjaijai
Dutta, Sanghita
author Jamir, Yangersenba
author_facet Jamir, Yangersenba
Kharkamni, Longjaijai
Dutta, Sanghita
author_role author
author2 Kharkamni, Longjaijai
Dutta, Sanghita
author2_role author
author
dc.contributor.none.fl_str_mv Council of Scientific and Industrial Research, India
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Ring of complex-valued continuous functions
Z-ideals
Absolutely convex ideals
zβ[A(X)]c-ideals
Hull-kernel topology
Structure space
topic Ring of complex-valued continuous functions
Z-ideals
Absolutely convex ideals
zβ[A(X)]c-ideals
Hull-kernel topology
Structure space
description [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.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/227678
url https://riunet.upv.es/handle/10251/227678
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/html
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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