The one-sided inverse along an element in semigroups and rings
Autor(a) principal: | |
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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/1822/50142 |
Resumo: | The concept of the inverse along an element was introduced by Mary in 2011. Later, Zhu et al. introduced the one-sided inverse along an element. In this paper, we first give a new existence criterion for the one-sided inverse along a product and characterize the existence of Moore–Penrose inverse by means of one-sided invertibility of certain element in a ring. In addition, we show that a∈ S † ⋂ S # if and only if (a∗a)k is invertible along a if and only if (aa∗)k is invertible along a in a ∗ -monoid S, where k is an arbitrary given positive integer. Finally, we prove that the inverse of a along aa ∗ coincides with the core inverse of a under the condition a∈ S { 1 , 4 } in a ∗ -monoid S. |
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The one-sided inverse along an element in semigroups and ringsInverse along an elementRingssemigroupsVon Neumann regularityScience & TechnologyThe concept of the inverse along an element was introduced by Mary in 2011. Later, Zhu et al. introduced the one-sided inverse along an element. In this paper, we first give a new existence criterion for the one-sided inverse along a product and characterize the existence of Moore–Penrose inverse by means of one-sided invertibility of certain element in a ring. In addition, we show that a∈ S † ⋂ S # if and only if (a∗a)k is invertible along a if and only if (aa∗)k is invertible along a in a ∗ -monoid S, where k is an arbitrary given positive integer. Finally, we prove that the inverse of a along aa ∗ coincides with the core inverse of a under the condition a∈ S { 1 , 4 } in a ∗ -monoid S.FCT - Fuel Cell Technologies Program(CXLX13-072)This research was supported 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) and the Foundation of Graduate Innovation Program of Jiangsu Province (No. KYZZ15-0049).info:eu-repo/semantics/publishedVersionBirkhäuser BaselUniversidade do MinhoJianlong ChenHonglin ZouHuihui ZhuPatrício, Pedro2017-10-012017-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/50142eng1660-54461660-545410.1007/s00009-017-1017-4info: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:RCAAP2023-07-21T11:59:14Zoai:repositorium.sdum.uminho.pt:1822/50142Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:48:59.343128Repositório 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 |
The one-sided inverse along an element in semigroups and rings |
title |
The one-sided inverse along an element in semigroups and rings |
spellingShingle |
The one-sided inverse along an element in semigroups and rings Jianlong Chen Inverse along an element Rings semigroups Von Neumann regularity Science & Technology |
title_short |
The one-sided inverse along an element in semigroups and rings |
title_full |
The one-sided inverse along an element in semigroups and rings |
title_fullStr |
The one-sided inverse along an element in semigroups and rings |
title_full_unstemmed |
The one-sided inverse along an element in semigroups and rings |
title_sort |
The one-sided inverse along an element in semigroups and rings |
author |
Jianlong Chen |
author_facet |
Jianlong Chen Honglin Zou Huihui Zhu Patrício, Pedro |
author_role |
author |
author2 |
Honglin Zou Huihui Zhu Patrício, Pedro |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Jianlong Chen Honglin Zou Huihui Zhu Patrício, Pedro |
dc.subject.por.fl_str_mv |
Inverse along an element Rings semigroups Von Neumann regularity Science & Technology |
topic |
Inverse along an element Rings semigroups Von Neumann regularity Science & Technology |
description |
The concept of the inverse along an element was introduced by Mary in 2011. Later, Zhu et al. introduced the one-sided inverse along an element. In this paper, we first give a new existence criterion for the one-sided inverse along a product and characterize the existence of Moore–Penrose inverse by means of one-sided invertibility of certain element in a ring. In addition, we show that a∈ S † ⋂ S # if and only if (a∗a)k is invertible along a if and only if (aa∗)k is invertible along a in a ∗ -monoid S, where k is an arbitrary given positive integer. Finally, we prove that the inverse of a along aa ∗ coincides with the core inverse of a under the condition a∈ S { 1 , 4 } in a ∗ -monoid S. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-10-01 2017-10-01T00:00:00Z |
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 |
http://hdl.handle.net/1822/50142 |
url |
http://hdl.handle.net/1822/50142 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1660-5446 1660-5454 10.1007/s00009-017-1017-4 |
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 |
Birkhäuser Basel |
publisher.none.fl_str_mv |
Birkhäuser Basel |
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) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132253446471680 |