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dc.contributor.author | Acharyya, Sudip Kumar | es_ES |
dc.contributor.author | Chattopadhyay, Kshitish Chandra | es_ES |
dc.contributor.author | Rooj, Pritam | es_ES |
dc.date.accessioned | 2015-05-13T12:43:16Z | |
dc.date.available | 2015-05-13T12:43:16Z | |
dc.date.issued | 2015-04-01 | |
dc.identifier.issn | 1576-9402 | |
dc.identifier.uri | http://hdl.handle.net/10251/50178 | |
dc.description.abstract | [EN] Suppose F is a totally ordered field equipped with its order topology and X a completely F-regular topological space. Suppose P is an ideal of closed sets in X and X is locally-P. Let CP(X, F) = {f : X ! F | f is continuous on X and its support belongs to P} and CP∞ (X, F) = {f 2 CP(X, F) | 8" > 0 in F, clX{x 2 X : |f(x)| > "} 2 P}. Then CP(X, F) is a Noetherian ring if and only if CP∞ (X, F) is a Noetherian ring if and only if X is a finite set. The fact that a locally compact Hausdorff space X is finite if and only if the ring CK(X) is Noetherian if and only if the ring C∞(X) is Noetherian, follows as a particular case on choosing F = R and P = the ideal of all compact sets in X. On the other hand if one takes F = R and P = the ideal of closed relatively pseudocompact subsets of X, then it follows that a locally pseudocompact space X is finite if and only if the ring C (X) of all real valued continuous functions on X with pseudocompact support is Noetherian if and only if the ring C ∞ (X) = {f 2 C(X) | 8" > 0, clX{x 2 X : |f(x)| > "} is pseudocompact } is Noetherian. Finally on choosing F = R and P = the ideal of all closed sets in X, it follows that: X is finite if and only if the ring C(X) is Noetherian if and only if the ring C∗(X) is Noetherian. | es_ES |
dc.description.sponsorship | The third author thanks the UGC, New Delhi-110002, India, for financial support | |
dc.language | Inglés | es_ES |
dc.publisher | Editorial 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 | Noetherian ring | es_ES |
dc.subject | Artinian ring | es_ES |
dc.subject | Totally ordered field | es_ES |
dc.subject | Zero-dimensional space | es_ES |
dc.subject | Pseudocompact support | es_ES |
dc.subject | Relatively pseudocompact support | es_ES |
dc.title | A generalized version of the rings CK (X) and C∞(X)– an enquery about when they become Noetheri | es_ES |
dc.type | Artículo | es_ES |
dc.date.updated | 2015-05-13T09:42:33Z | |
dc.identifier.doi | 10.4995/agt.2015.3247 | |
dc.rights.accessRights | Abierto | es_ES |
dc.description.bibliographicCitation | Acharyya, SK.; Chattopadhyay, KC.; Rooj, P. (2015). A generalized version of the rings CK (X) and C∞(X)– an enquery about when they become Noetheri. Applied General Topology. 16(1):81-87. https://doi.org/10.4995/agt.2015.3247 | es_ES |
dc.description.accrualMethod | SWORD | es_ES |
dc.relation.publisherversion | https://doi.org/10.4995/agt.2015.3247 | es_ES |
dc.description.upvformatpinicio | 81 | es_ES |
dc.description.upvformatpfin | 87 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 16 | |
dc.description.issue | 1 | |
dc.identifier.eissn | 1989-4147 | |
dc.contributor.funder | University Grants Commission, India | |
dc.description.references | S. K. Acharyya and S. K. Ghosh, Functions in C(X) with support lying on a class of subsets of X, Topology Proc. 35 (2010), 127-148. | es_ES |
dc.description.references | I. Gelfand and A. Kolmogoroff, On Rings of Continuous Functions on topological spaces, Dokl. Akad. Nauk SSSR 22 (1939), 11-15. | es_ES |
dc.description.references | C. W. Kohls, Ideals in rings of Continuous Functions, Fund. Math. 45 (1957), 28-50. | es_ES |
dc.description.references | C. W. Kohls, Prime ideals in rings of Continuous Functions, Illinois. J. Math. 2 (1958), 505-536. | es_ES |