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When is the super socle of C(X) prime?

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When is the super socle of C(X) prime?

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dc.contributor.author Ghasemzadeh, S. es_ES
dc.contributor.author Namdari, M. es_ES
dc.date.accessioned 2019-04-04T09:59:34Z
dc.date.available 2019-04-04T09:59:34Z
dc.date.issued 2019-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/118973
dc.description.abstract [EN] Let SCF(X) denote the ideal of C(X) consisting of functions which are zero everywhere except on a countable number of points of X. It is generalization of the socle of C(X) denoted by CF(X). Using this concept we extend some of the basic results concerning CF(X) to SCF(X). In particular, we characterize the spaces X such that SCF(X) is a prime ideal in C(X) (note, CF(X) is never a prime ideal in C(X)). This may be considered as an advantage of SCF(X) over C(X). We are also interested in characterizing topological spaces X such that Cc(X) =R+SCF(X), where Cc(X) denotes the subring of C(X) consisting of functions with countable image. es_ES
dc.description.sponsorship The authors would like to thank professor O. A. S. Karamzadeh for introducing the concept of super socle of C(X) and for his helpful suggestions. The authors are also indebted to the well-informed, meticulous referee for reading the article carefully and giving valuable and constructive comments. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Super socle of C(X) es_ES
dc.subject Countably isolated point es_ES
dc.subject Countably discrete space es_ES
dc.subject Cocountably-disconnected space es_ES
dc.subject One-point Lindelöffication es_ES
dc.title When is the super socle of C(X) prime? es_ES
dc.type Artículo es_ES
dc.date.updated 2019-04-04T06:30:50Z
dc.identifier.doi 10.4995/agt.2019.10731
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Ghasemzadeh, S.; Namdari, M. (2019). When is the super socle of C(X) prime?. Applied General Topology. 20(1):231-236. https://doi.org/10.4995/agt.2019.10731 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2019.10731 es_ES
dc.description.upvformatpinicio 231 es_ES
dc.description.upvformatpfin 236 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 20
dc.description.issue 1
dc.identifier.eissn 1989-4147
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