Centralizer's applications to the inverse along an element
Autor(a) principal: | |
---|---|
Data de Publicação: | 2017 |
Outros Autores: | , , |
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. |
id |
RCAP_6c41c10215399c8e35f46a0c21f3dc6d |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/50137 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799132441921716224 |