Characterizations of special clean elements and applications
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
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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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 |
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 |
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1799132734950473728 |