Generalized inverses and their relations with clean decompositions

Detalhes bibliográficos
Autor(a) principal: Huihui Zhu
Data de Publicação: 2019
Outros Autores: Honglin Zou, 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/1822/64193
Resumo: An element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e and a unit u such that an = e + u is both a strongly clean decomposition and a special clean decomposition, for some positive integer n. Also, the existence of the Moore-Penrose and group inverses is related to the existence of certain - clean decompositions.
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spelling Generalized inverses and their relations with clean decompositionsDrazin inverseGroup inverseMoore-Penrose inverseStrongly clean decompositionSpecial clean decompositionCiências Naturais::MatemáticasScience & TechnologyAn element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e and a unit u such that an = e + u is both a strongly clean decomposition and a special clean decomposition, for some positive integer n. Also, the existence of the Moore-Penrose and group inverses is related to the existence of certain - clean decompositions.This research is supported by the Natural Science Foundation of Anhui Province (No. 1808085QA16), the Fundamental Research Funds for the Central Universities (No. JZ2018HGTB0233), China Postdoctoral Science Foundation (No. 2018M632385) and the Portuguese Funds through FCT- ‘Fundação para a Ciência e a Tecnologia’, within the project UID/MAT/00013/2013.World Scientific PublishingUniversidade do MinhoHuihui ZhuHonglin ZouPatrício, Pedro2019-07-012019-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/64193eng0219-49881793-682910.1142/S0219498819501330info: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:RCAAP2023-07-21T12:41:25Zoai:repositorium.sdum.uminho.pt:1822/64193Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:38:24.246383Repositório 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 Generalized inverses and their relations with clean decompositions
title Generalized inverses and their relations with clean decompositions
spellingShingle Generalized inverses and their relations with clean decompositions
Huihui Zhu
Drazin inverse
Group inverse
Moore-Penrose inverse
Strongly clean decomposition
Special clean decomposition
Ciências Naturais::Matemáticas
Science & Technology
title_short Generalized inverses and their relations with clean decompositions
title_full Generalized inverses and their relations with clean decompositions
title_fullStr Generalized inverses and their relations with clean decompositions
title_full_unstemmed Generalized inverses and their relations with clean decompositions
title_sort Generalized inverses and their relations with clean decompositions
author Huihui Zhu
author_facet Huihui Zhu
Honglin Zou
Patrício, Pedro
author_role author
author2 Honglin Zou
Patrício, Pedro
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Huihui Zhu
Honglin Zou
Patrício, Pedro
dc.subject.por.fl_str_mv Drazin inverse
Group inverse
Moore-Penrose inverse
Strongly clean decomposition
Special clean decomposition
Ciências Naturais::Matemáticas
Science & Technology
topic Drazin inverse
Group inverse
Moore-Penrose inverse
Strongly clean decomposition
Special clean decomposition
Ciências Naturais::Matemáticas
Science & Technology
description An element a in a ring R is called clean if it is the sum of an idempotent e and a unit u. Such a clean decomposition a = e + u is said to be strongly clean if eu = ue and special clean if aR eR = (0). In this paper, we prove that a is Drazin invertible if and only if there exists an idempotent e and a unit u such that an = e + u is both a strongly clean decomposition and a special clean decomposition, for some positive integer n. Also, the existence of the Moore-Penrose and group inverses is related to the existence of certain - clean decompositions.
publishDate 2019
dc.date.none.fl_str_mv 2019-07-01
2019-07-01T00:00:00Z
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/1822/64193
url https://hdl.handle.net/1822/64193
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0219-4988
1793-6829
10.1142/S0219498819501330
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 World Scientific Publishing
publisher.none.fl_str_mv World Scientific Publishing
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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