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Invertibles in topological rings: a new approach

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Invertibles in topological rings: a new approach

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dc.contributor.author García-Pacheco, Francisco Javier es_ES
dc.contributor.author Miralles, Alejandro es_ES
dc.contributor.author Murillo Arcila, Marina es_ES
dc.date.accessioned 2023-11-15T19:01:18Z
dc.date.available 2023-11-15T19:01:18Z
dc.date.issued 2022-01 es_ES
dc.identifier.issn 1578-7303 es_ES
dc.identifier.uri http://hdl.handle.net/10251/199838
dc.description.abstract [EN] Every element in the boundary of the group of invertibles of a Banach algebra is a topological zero divisor. We extend this result to the scope of topological rings. In particular, we define a new class of semi-normed rings, called almost absolutely semi-normed rings, which strictly includes the class of absolutely semi-valued rings, and prove that every element in the boundary of the group of invertibles of a complete almost absolutely semi-normed ring is a topological zero divisor. To achieve all these, we have to previously entail an exhaustive study of topological divisors of zero in topological rings. In addition, it is also well known that the group of invertibles is open and the inversion map is continuous and C-differentiable in a Banach algebra. We also extend these results to the setting of complete normed rings. Finally, this study allows us to generalize the point, continuous and residual spectra to the scope of Banach algebras. es_ES
dc.description.sponsorship The authors would like to thank the reviewers for their valuable comments and remarks which have contributed to improve the presentation and quality of the manuscript. The first author has been supported by Research Grant PGC-101514-B-I00 awarded by the Ministry of Science, Innovation and Universities of Spain, and by the 2014-2020 ERDF Operational Programme and by the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia with Project reference: FEDER-UCA18-105867 and Ministerio de Educacion y Ciencia (Grant number MTM2016-75963-P). The second author has been supported by Project PGC2018-094431-B-100 (MICINN. Spain) and Project 8059/2019 (Universitat Jaume I). The third author is supported by MCIN/AEI/10.13039/501100011033, Project PID2019-105011GB-I00, and by Generalitat Valenciana, Project PROMETEU/2021/070. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Spectrum es_ES
dc.subject Rings es_ES
dc.subject Algebras es_ES
dc.subject Zero divisor es_ES
dc.subject Invertibles es_ES
dc.subject Operator es_ES
dc.title Invertibles in topological rings: a new approach es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s13398-021-01183-4 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-094431-B-I00/ES/ESPACIOS DE FUNCIONES: FUNCIONES ANALITICAS Y OPERADORES DE COMPOSICION. RENORMAMIENTOS Y TOPOLOGIA DESCRIPTIVA/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//PROMETEO%2F2021%2F070//Análisis funcional, dinámica de operadores y aplicaciones/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Junta de Andalucía//FEDER-UCA18-105867/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MECD//MTM2016-75963-P//Dinámica de operadores/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MCIU//PGC-101514-B-I00/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJI//8059%2F2019/ es_ES
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation García-Pacheco, FJ.; Miralles, A.; Murillo Arcila, M. (2022). Invertibles in topological rings: a new approach. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 116(1):1-17. https://doi.org/10.1007/s13398-021-01183-4 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s13398-021-01183-4 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 17 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 116 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\455733 es_ES
dc.contributor.funder Junta de Andalucía es_ES
dc.contributor.funder Universitat Jaume I es_ES
dc.contributor.funder GENERALITAT VALENCIANA es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Educación, Cultura y Deporte es_ES
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades es_ES
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