A note on clean elements and inverses along an element

Detalhes bibliográficos
Autor(a) principal: Zhu, Huihui
Data de Publicação: 2018
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/1822/66087
Resumo: Let R be an associative ring with unity 1 and let a, d is an element of R. An element a is an element of R is called invertible along d if there exists unique a(parallel to d) such that a(parallel to d) ad = d = daa(parallel to d) and a(parallel to d )is an element of dR boolean AND Rd (see [6, Definition 4]). In this note, we present new characterizations for the existence of a(parallel to d )by clean decompositions of ad and da. As applications, existence criteria for the Drazin inverse and the group inverse are given.
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spelling A note on clean elements and inverses along an elementinverses along an elementone-sided inverses along an elementclean elementsstrongly clean decompositionsspecial clean decompositionsCiências Naturais::MatemáticasScience & TechnologyLet R be an associative ring with unity 1 and let a, d is an element of R. An element a is an element of R is called invertible along d if there exists unique a(parallel to d) such that a(parallel to d) ad = d = daa(parallel to d) and a(parallel to d )is an element of dR boolean AND Rd (see [6, Definition 4]). In this note, we present new characterizations for the existence of a(parallel to d )by clean decompositions of ad and da. As applications, existence criteria for the Drazin inverse and the group inverse are given.The authors are highly grateful to the referee for his/her valuable comments and suggestions which greatly improved this paper. This research is supported by the National Natural Science Foundation of China (No. 11801124), the Fundamental Research Funds for the Central Universities (No. JZ2018HGTB0233) and the Natural Science Foundation of Anhui Province (No. 1808085QA16), and the Portuguese Funds through FCT-'Fundacao para a Ciencia e a Tecnologia', within the project UID-MAT-00013/2013.University of Niš. Faculty of Sciences and MathematicsUniversidade do MinhoZhu, HuihuiPatrício, Pedro20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/66087engZhu, H., & Patrício, P. (2018). A note on clean elements and inverses along an element. Filomat. National Library of Serbia. http://doi.org/10.2298/fil1812285z0354-51802406-093310.2298/FIL1812285Zhttp://www.doiserbia.nb.rs/img/doi/0354-5180/2018/0354-51801812285Z.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:RCAAP2023-10-28T01:18:12Zoai:repositorium.sdum.uminho.pt:1822/66087Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:04:49.887723Repositório 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 A note on clean elements and inverses along an element
title A note on clean elements and inverses along an element
spellingShingle A note on clean elements and inverses along an element
Zhu, Huihui
inverses along an element
one-sided inverses along an element
clean elements
strongly clean decompositions
special clean decompositions
Ciências Naturais::Matemáticas
Science & Technology
title_short A note on clean elements and inverses along an element
title_full A note on clean elements and inverses along an element
title_fullStr A note on clean elements and inverses along an element
title_full_unstemmed A note on clean elements and inverses along an element
title_sort A note on clean elements and inverses along an element
author Zhu, Huihui
author_facet Zhu, Huihui
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 Zhu, Huihui
Patrício, Pedro
dc.subject.por.fl_str_mv inverses along an element
one-sided inverses along an element
clean elements
strongly clean decompositions
special clean decompositions
Ciências Naturais::Matemáticas
Science & Technology
topic inverses along an element
one-sided inverses along an element
clean elements
strongly clean decompositions
special clean decompositions
Ciências Naturais::Matemáticas
Science & Technology
description Let R be an associative ring with unity 1 and let a, d is an element of R. An element a is an element of R is called invertible along d if there exists unique a(parallel to d) such that a(parallel to d) ad = d = daa(parallel to d) and a(parallel to d )is an element of dR boolean AND Rd (see [6, Definition 4]). In this note, we present new characterizations for the existence of a(parallel to d )by clean decompositions of ad and da. As applications, existence criteria for the Drazin inverse and the group inverse are given.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
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/1822/66087
url https://hdl.handle.net/1822/66087
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Zhu, H., & Patrício, P. (2018). A note on clean elements and inverses along an element. Filomat. National Library of Serbia. http://doi.org/10.2298/fil1812285z
0354-5180
2406-0933
10.2298/FIL1812285Z
http://www.doiserbia.nb.rs/img/doi/0354-5180/2018/0354-51801812285Z.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 Sciences and Mathematics
publisher.none.fl_str_mv University of Niš. Faculty of Sciences 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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