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Ideals in B1(X) and residue class rings of B1(X) modulo an ideal

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Ideals in B1(X) and residue class rings of B1(X) modulo an ideal

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dc.contributor.author Deb Ray, A. es_ES
dc.contributor.author Mondal, Atanu es_ES
dc.date.accessioned 2019-10-03T07:21:33Z
dc.date.available 2019-10-03T07:21:33Z
dc.date.issued 2019-10-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/127130
dc.description.abstract [EN] This paper explores the duality between ideals of the ring B1(X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called ZB-filters, on X. As a natural outcome of this study, it is observed that B1(X) is a Gelfand ring but non-Noetherian in general. Introducing fixed and free maximal ideals in the context of B1(X), complete descriptions of the fixed maximal ideals of both B1(X) and B1* (X) are obtained. Though free maximal ideals of B1(X) and those of B1* (X) do not show any relationship in general, their counterparts, i.e., the fixed maximal ideals obey natural relations. It is proved here that for a perfectly normal T1 space X, free maximal ideals of B1(X) are determined by a typical class of Baire one functions. In the concluding part of this paper, we study residue class ring of B1(X) modulo an ideal, with special emphasize on real and hyper real maximal ideals of B1(X). 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 ZB- filter es_ES
dc.subject ZB -ultrafilter es_ES
dc.subject ZB -ideal es_ES
dc.subject Fixed ideal es_ES
dc.subject Free ideal es_ES
dc.subject Residue class ring es_ES
dc.subject Real maximal ideal es_ES
dc.subject Hyper real maximal ideal es_ES
dc.title Ideals in B1(X) and residue class rings of B1(X) modulo an ideal es_ES
dc.type Artículo es_ES
dc.date.updated 2019-10-03T06:47:15Z
dc.identifier.doi 10.4995/agt.2019.11417
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Deb Ray, A.; Mondal, A. (2019). Ideals in B1(X) and residue class rings of B1(X) modulo an ideal. Applied General Topology. 20(2):379-393. https://doi.org/10.4995/agt.2019.11417 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2019.11417 es_ES
dc.description.upvformatpinicio 379 es_ES
dc.description.upvformatpfin 393 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 20
dc.description.issue 2
dc.identifier.eissn 1989-4147
dc.description.references A. Deb Ray and A. Mondal, On rings of Baire one functions, Applied Gen. Topol. 20, no. 1 (2019), 237-249. https://doi.org/10.4995/agt.2019.10776 es_ES
dc.description.references J. P. Fenecios and E. A. Cabral, On some properties of Baire-1 functions, Int. Journal of Math. Analysis 7, no. 8 (2013), 393-402. https://doi.org/10.12988/ijma.2013.13035 es_ES
dc.description.references L. Gillman and M. Jerison, Rings of Continuous Functions, New York: Van Nostrand Reinhold Co., 1960. https://doi.org/10.1007/978-1-4615-7819-2 es_ES
dc.description.references J. R. Munkres, Topology, Second edition, Pearson Education, Delhi, 2003. es_ES
dc.description.references L. Vesely, Characterization of Baire-one functions between topological spaces, Acta Universitatis Carolinae. Mathematica et Physica 33, no. 2 (1992), 143-156. es_ES


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