Centralizer's applications to the inverse along an element

Detalhes bibliográficos
Autor(a) principal: Huihui Zhu
Data de Publicação: 2017
Outros Autores: Jianlong Chen, Patrício, Pedro, Mary, Xavier
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/50137
Resumo: In this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elements. Also, we prove that a left inverse of a along d coincides with a right inverse of a along d, provided that they both exist. Then, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore–Penrose inverse of a regular element by one-sided invertibilities in a ring with involution.
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spelling Centralizer's applications to the inverse along an elementAbsorption lawsCentralizersInverses along an elementLeft (Right) inverses along an elementMoore–Penrose inversesReverse order lawsScience & TechnologyIn this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elements. Also, we prove that a left inverse of a along d coincides with a right inverse of a along d, provided that they both exist. Then, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore–Penrose inverse of a regular element by one-sided invertibilities in a ring with involution.FCT - Natural Science Foundation of Jiangsu Province(UID-MAT-00013/2013)This research was carried out by the first author during his visit to the Department of Mathematics and Applications, University of Minho, Portugal. He gratefully acknowledges the financial support of China Scholarship Council. This research is also supported 11 by the National Natural Science Foundation of China (No. 11371089), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120092110020), the Natural Science Foundation of Jiangsu Province (No. BK20141327), the Scientific Innovation Research of College Graduates in Jiangsu Province (No. CXLX13-072), the Scientific Research Foundation of Graduate School of Southeast University, the FEDER Funds through Programa Operacional Factores de Competitividade-COMPETE’, the Portuguese Funds through FCT- ‘Funda¸c˜ao para a Ciˆencia e a Tecnologia’, within the project UID-MAT-00013/2013.info:eu-repo/semantics/publishedVersionElsevierUniversidade do MinhoHuihui ZhuJianlong ChenPatrício, PedroMary, Xavier2017-12-152017-12-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/50137eng0096-300310.1016/j.amc.2017.07.046info: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:RCAAP2023-07-21T12:11:45Zoai:repositorium.sdum.uminho.pt:1822/50137Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:03:33.506016Repositório 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 Centralizer's applications to the inverse along an element
title Centralizer's applications to the inverse along an element
spellingShingle Centralizer's applications to the inverse along an element
Huihui Zhu
Absorption laws
Centralizers
Inverses along an element
Left (Right) inverses along an element
Moore–Penrose inverses
Reverse order laws
Science & Technology
title_short Centralizer's applications to the inverse along an element
title_full Centralizer's applications to the inverse along an element
title_fullStr Centralizer's applications to the inverse along an element
title_full_unstemmed Centralizer's applications to the inverse along an element
title_sort Centralizer's applications to the inverse along an element
author Huihui Zhu
author_facet Huihui Zhu
Jianlong Chen
Patrício, Pedro
Mary, Xavier
author_role author
author2 Jianlong Chen
Patrício, Pedro
Mary, Xavier
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Huihui Zhu
Jianlong Chen
Patrício, Pedro
Mary, Xavier
dc.subject.por.fl_str_mv Absorption laws
Centralizers
Inverses along an element
Left (Right) inverses along an element
Moore–Penrose inverses
Reverse order laws
Science & Technology
topic Absorption laws
Centralizers
Inverses along an element
Left (Right) inverses along an element
Moore–Penrose inverses
Reverse order laws
Science & Technology
description In this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elements. Also, we prove that a left inverse of a along d coincides with a right inverse of a along d, provided that they both exist. Then, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore–Penrose inverse of a regular element by one-sided invertibilities in a ring with involution.
publishDate 2017
dc.date.none.fl_str_mv 2017-12-15
2017-12-15T00:00:00Z
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 http://hdl.handle.net/1822/50137
url http://hdl.handle.net/1822/50137
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0096-3003
10.1016/j.amc.2017.07.046
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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