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Drazin-Moore-Penrose invertibility in rings

Bibliographic Details
Main Author: Patrício, Pedro
Publication Date: 2004
Other Authors: Puystjens, Roland
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/1516
Summary: Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal. As an application we consider the ring of square matrices of order $m$ over a projective free ring $R$ with involution such that $R^m$ is a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.
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spelling Drazin-Moore-Penrose invertibility in ringsDrazinMoore-PenroseGeneralized inversesEP elementsCore nilpotent decompositionFitting decompositionScience & TechnologyCharacterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal. As an application we consider the ring of square matrices of order $m$ over a projective free ring $R$ with involution such that $R^m$ is a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI).Centro de Matemática da Universidade do Minho (CMAT).ElsevierUniversidade do MinhoPatrício, PedroPuystjens, Roland20042004-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/1516eng"Linear algebra and its applications". ISSN 0024-3795. 389 (2004) 159-173.0024-379510.1016/j.laa.2004.04.006info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-04-12T05:06:40Zoai:repositorium.sdum.uminho.pt:1822/1516Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T16:04:40.143655Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Drazin-Moore-Penrose invertibility in rings
title Drazin-Moore-Penrose invertibility in rings
spellingShingle Drazin-Moore-Penrose invertibility in rings
Patrício, Pedro
Drazin
Moore-Penrose
Generalized inverses
EP elements
Core nilpotent decomposition
Fitting decomposition
Science & Technology
title_short Drazin-Moore-Penrose invertibility in rings
title_full Drazin-Moore-Penrose invertibility in rings
title_fullStr Drazin-Moore-Penrose invertibility in rings
title_full_unstemmed Drazin-Moore-Penrose invertibility in rings
title_sort Drazin-Moore-Penrose invertibility in rings
author Patrício, Pedro
author_facet Patrício, Pedro
Puystjens, Roland
author_role author
author2 Puystjens, Roland
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Patrício, Pedro
Puystjens, Roland
dc.subject.por.fl_str_mv Drazin
Moore-Penrose
Generalized inverses
EP elements
Core nilpotent decomposition
Fitting decomposition
Science & Technology
topic Drazin
Moore-Penrose
Generalized inverses
EP elements
Core nilpotent decomposition
Fitting decomposition
Science & Technology
description Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal. As an application we consider the ring of square matrices of order $m$ over a projective free ring $R$ with involution such that $R^m$ is a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.
publishDate 2004
dc.date.none.fl_str_mv 2004
2004-01-01T00:00:00Z
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/1822/1516
url https://hdl.handle.net/1822/1516
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Linear algebra and its applications". ISSN 0024-3795. 389 (2004) 159-173.
0024-3795
10.1016/j.laa.2004.04.006
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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