Group-regular rings

Detalhes bibliográficos
Autor(a) principal: Mary, Xavier
Data de Publicação: 2019
Outros Autores: Patrício, Pedro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/72217
Resumo: We propose different generalizations of unit-regularity of elements in general rings (non necessarily unital rings). We then study general rings for which all elements have these properties. We notably compare them with unit-regular ideals and general rings with stable range one. We also prove that these rings are morphic rings.
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spelling Group-regular ringsUnit-regular elementStrongly regular (group) elementGeneral ringAdjoint semigroupMorphic ringStable range oneCiências Naturais::MatemáticasScience & TechnologyWe propose different generalizations of unit-regularity of elements in general rings (non necessarily unital rings). We then study general rings for which all elements have these properties. We notably compare them with unit-regular ideals and general rings with stable range one. We also prove that these rings are morphic rings.This research has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01), and was also partially supported by FCT-'Fundação para a Ciência e a Tecnologia', within the project UID/MAT/00013/2013.University of Niš. Faculty of Science and MathematicsUniversidade do MinhoMary, XavierPatrício, Pedro20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/72217engMary, X., & Patrício, P. (2019). Group-regular rings. Filomat. National Library of Serbia. http://doi.org/10.2298/fil1911551m0354-51802406-093310.2298/FIL1911551Mhttps://www.pmf.ni.ac.rs/filomat-content/2019/33-11/33-11-22-9842.pdfinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-10-28T01:18:08Zoai:repositorium.sdum.uminho.pt:1822/72217Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:54:46.856221Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Group-regular rings
title Group-regular rings
spellingShingle Group-regular rings
Mary, Xavier
Unit-regular element
Strongly regular (group) element
General ring
Adjoint semigroup
Morphic ring
Stable range one
Ciências Naturais::Matemáticas
Science & Technology
title_short Group-regular rings
title_full Group-regular rings
title_fullStr Group-regular rings
title_full_unstemmed Group-regular rings
title_sort Group-regular rings
author Mary, Xavier
author_facet Mary, Xavier
Patrício, Pedro
author_role author
author2 Patrício, Pedro
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Mary, Xavier
Patrício, Pedro
dc.subject.por.fl_str_mv Unit-regular element
Strongly regular (group) element
General ring
Adjoint semigroup
Morphic ring
Stable range one
Ciências Naturais::Matemáticas
Science & Technology
topic Unit-regular element
Strongly regular (group) element
General ring
Adjoint semigroup
Morphic ring
Stable range one
Ciências Naturais::Matemáticas
Science & Technology
description We propose different generalizations of unit-regularity of elements in general rings (non necessarily unital rings). We then study general rings for which all elements have these properties. We notably compare them with unit-regular ideals and general rings with stable range one. We also prove that these rings are morphic rings.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/72217
url https://hdl.handle.net/1822/72217
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mary, X., & Patrício, P. (2019). Group-regular rings. Filomat. National Library of Serbia. http://doi.org/10.2298/fil1911551m
0354-5180
2406-0933
10.2298/FIL1911551M
https://www.pmf.ni.ac.rs/filomat-content/2019/33-11/33-11-22-9842.pdf
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv University of Niš. Faculty of Science and Mathematics
publisher.none.fl_str_mv University of Niš. Faculty of Science and Mathematics
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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