Generalized inverses and their relations with clean decompositions
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
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/1822/64193 |
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. |
id |
RCAP_e6381d6bbdffcd0f20e80331621b03d3 |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/64193 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799132920644894720 |