Characterizations and representations of left and right hybrid (b, c)-inverses in rings

Detalhes bibliográficos
Autor(a) principal: Zhu, Huihui
Data de Publicação: 2021
Outros Autores: Wu, Liyun, Peng, Fei, 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/1822/80234
Resumo: Let R be an associative ring with unity 1 and let a, b ,c is an element of R. In this paper, several characterizations for left and right hybrid (b, c)-inverses of a are derived. Moreover, their formulae are given by regularities of certain elements. Then, we give characterizations of right (b, c)-inverses and right annihilator (b, c)-inverses of the product of three elements. Finally, relations among the right hybrid (b, c)-inverse of paq, the right (qb, c)-inverse of aq and the right annihilator (b, cp)-inverse of aq are given.
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spelling Characterizations and representations of left and right hybrid (b, c)-inverses in rings(b, c)-inversesHybrid (b, c)-inversesAnnihilatorsIdealsRingsCiências Naturais::MatemáticasScience & TechnologyLet R be an associative ring with unity 1 and let a, b ,c is an element of R. In this paper, several characterizations for left and right hybrid (b, c)-inverses of a are derived. Moreover, their formulae are given by regularities of certain elements. Then, we give characterizations of right (b, c)-inverses and right annihilator (b, c)-inverses of the product of three elements. Finally, relations among the right hybrid (b, c)-inverse of paq, the right (qb, c)-inverse of aq and the right annihilator (b, cp)-inverse of aq are given.The authors are highly grateful to the referee for his/her valuable comments and suggestions which led to improvements of this paper. This research is supported by the National Natural Science Foundation of China (no. 11801124), China Postdoctoral Science Foundation (no. 2020M671068) and the Natural Science Foundation of Anhui Province (no. 1808085QA16) and Portuguese Funds through FCT (Fundcao para a Ciencia e a Tecnologia) within the Projects UIDB/00013/2020 and UIDP/00013/2020.Springer VerlagUniversidade do MinhoZhu, HuihuiWu, LiyunPeng, FeiPatrício, Pedro20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/80234engZhu, H., Wu, L., Peng, F. et al. Characterizations and representations of left and right hybrid (b, c)-inverses in rings. RACSAM 115, 22 (2021). https://doi.org/10.1007/s13398-020-00956-71578-73031579-150510.1007/s13398-020-00956-7info: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:RCAAP2023-07-21T12:12:02Zoai:repositorium.sdum.uminho.pt:1822/80234Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:03:55.774981Repositório 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 Characterizations and representations of left and right hybrid (b, c)-inverses in rings
title Characterizations and representations of left and right hybrid (b, c)-inverses in rings
spellingShingle Characterizations and representations of left and right hybrid (b, c)-inverses in rings
Zhu, Huihui
(b, c)-inverses
Hybrid (b, c)-inverses
Annihilators
Ideals
Rings
Ciências Naturais::Matemáticas
Science & Technology
title_short Characterizations and representations of left and right hybrid (b, c)-inverses in rings
title_full Characterizations and representations of left and right hybrid (b, c)-inverses in rings
title_fullStr Characterizations and representations of left and right hybrid (b, c)-inverses in rings
title_full_unstemmed Characterizations and representations of left and right hybrid (b, c)-inverses in rings
title_sort Characterizations and representations of left and right hybrid (b, c)-inverses in rings
author Zhu, Huihui
author_facet Zhu, Huihui
Wu, Liyun
Peng, Fei
Patrício, Pedro
author_role author
author2 Wu, Liyun
Peng, Fei
Patrício, Pedro
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Zhu, Huihui
Wu, Liyun
Peng, Fei
Patrício, Pedro
dc.subject.por.fl_str_mv (b, c)-inverses
Hybrid (b, c)-inverses
Annihilators
Ideals
Rings
Ciências Naturais::Matemáticas
Science & Technology
topic (b, c)-inverses
Hybrid (b, c)-inverses
Annihilators
Ideals
Rings
Ciências Naturais::Matemáticas
Science & Technology
description Let R be an associative ring with unity 1 and let a, b ,c is an element of R. In this paper, several characterizations for left and right hybrid (b, c)-inverses of a are derived. Moreover, their formulae are given by regularities of certain elements. Then, we give characterizations of right (b, c)-inverses and right annihilator (b, c)-inverses of the product of three elements. Finally, relations among the right hybrid (b, c)-inverse of paq, the right (qb, c)-inverse of aq and the right annihilator (b, cp)-inverse of aq are given.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
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/1822/80234
url https://hdl.handle.net/1822/80234
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Zhu, H., Wu, L., Peng, F. et al. Characterizations and representations of left and right hybrid (b, c)-inverses in rings. RACSAM 115, 22 (2021). https://doi.org/10.1007/s13398-020-00956-7
1578-7303
1579-1505
10.1007/s13398-020-00956-7
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 Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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
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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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