Characterizations of special clean elements and applications

Detalhes bibliográficos
Autor(a) principal: Mary, Xavier
Data de Publicação: 2020
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/1822/80236
Resumo: We prove that special clean decompositions of a given element of a ring are in one-to-one correspondence with the set of solutions of a simple equation in a corner ring. We then derive "constructive" proofs that in many rings, regular elements are special clean by solving this equation in specific cases. Other applications, such as uniqueness of decompositions, are given. Many examples of special clean decompositions of 2-2 matrices found by this methodology are also presented.
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spelling Characterizations of special clean elements and applicationsSpecial clean elementsUnit-regular elementsStrongly regular (group) elementsStable range 1Science & TechnologyWe prove that special clean decompositions of a given element of a ring are in one-to-one correspondence with the set of solutions of a simple equation in a corner ring. We then derive "constructive" proofs that in many rings, regular elements are special clean by solving this equation in specific cases. Other applications, such as uniqueness of decompositions, are given. Many examples of special clean decompositions of 2-2 matrices found by this methodology are also presented.The research at CMAT was partially financed by Portuguese Funds through FCT (Fundação para a Ciência e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020. It has also been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01).University of Niš. Faculty of Science and MathematicsUniversidade do MinhoMary, XavierPatrício, Pedro20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/80236engMary, X., & Patrício, P. (2020). Characterizations of special clean elements and applications. Filomat. National Library of Serbia. http://doi.org/10.2298/fil2014847m0354-51802406-093310.2298/FIL2014847Mhttps://doiserbia.nb.rs/Article.aspx?ID=0354-51802014847Minfo: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:RCAAP2023-10-28T01:18:24Zoai:repositorium.sdum.uminho.pt:1822/80236Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:25:10.720760Repositório 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 Characterizations of special clean elements and applications
title Characterizations of special clean elements and applications
spellingShingle Characterizations of special clean elements and applications
Mary, Xavier
Special clean elements
Unit-regular elements
Strongly regular (group) elements
Stable range 1
Science & Technology
title_short Characterizations of special clean elements and applications
title_full Characterizations of special clean elements and applications
title_fullStr Characterizations of special clean elements and applications
title_full_unstemmed Characterizations of special clean elements and applications
title_sort Characterizations of special clean elements and applications
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 Special clean elements
Unit-regular elements
Strongly regular (group) elements
Stable range 1
Science & Technology
topic Special clean elements
Unit-regular elements
Strongly regular (group) elements
Stable range 1
Science & Technology
description We prove that special clean decompositions of a given element of a ring are in one-to-one correspondence with the set of solutions of a simple equation in a corner ring. We then derive "constructive" proofs that in many rings, regular elements are special clean by solving this equation in specific cases. Other applications, such as uniqueness of decompositions, are given. Many examples of special clean decompositions of 2-2 matrices found by this methodology are also presented.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
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/1822/80236
url https://hdl.handle.net/1822/80236
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mary, X., & Patrício, P. (2020). Characterizations of special clean elements and applications. Filomat. National Library of Serbia. http://doi.org/10.2298/fil2014847m
0354-5180
2406-0933
10.2298/FIL2014847M
https://doiserbia.nb.rs/Article.aspx?ID=0354-51802014847M
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
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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
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