Generalized inverses, ideals, and projectors in rings

Autores
Morillas, Patricia Mariela
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring R with a unit 1 , 0. We prove that generalized inverses in R are related to idempotent group endomorphisms ρ : R → R, called projectors. We use these relations to give characterizations and existence conditions for {1}, {2}, and {1, 2}-inverses with any given principal/annihilator ideals. As a consequence, we obtain sufficient conditions for any right/left ideal of R to be a principal or an annihilator ideal of an idempotent element of R. We also study some particular generalized inverses: Drazin and (b, c) inverses, and (e, f) Moore-Penrose, e-core, f-dual core, w-core, dual v-core, right w-core, left dual v-core, and (p, q) inverses in rings with involution.
Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Materia
GENERALIZED INVERSE
RING
IDEAL
DIRECT SUM
PROJECTOR
INVOLUTION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/257862
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/257862
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Generalized inverses, ideals, and projectors in ringsMorillas, Patricia MarielaGENERALIZED INVERSERINGIDEALDIRECT SUMPROJECTORINVOLUTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring R with a unit 1 , 0. We prove that generalized inverses in R are related to idempotent group endomorphisms ρ : R → R, called projectors. We use these relations to give characterizations and existence conditions for {1}, {2}, and {1, 2}-inverses with any given principal/annihilator ideals. As a consequence, we obtain sufficient conditions for any right/left ideal of R to be a principal or an annihilator ideal of an idempotent element of R. We also study some particular generalized inverses: Drazin and (b, c) inverses, and (e, f) Moore-Penrose, e-core, f-dual core, w-core, dual v-core, right w-core, left dual v-core, and (p, q) inverses in rings with involution.Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaUniversity of Nis2024-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/257862Morillas, Patricia Mariela; Generalized inverses, ideals, and projectors in rings; University of Nis; Filomat; 38; 19; 4-2024; 6715-67410354-5180CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.pmf.ni.ac.rs/filomat-content/2024/38-19/FILOMAT%2038-19.htmlinfo:eu-repo/semantics/altIdentifier/url/https://www.pmf.ni.ac.rs/filomat-content/2024/38-19/38-19-7-22749.pdfinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/pdf/2304.06149info:eu-repo/semantics/altIdentifier/doi/10.2298/FIL2419715Minfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:09:27Zoai:ri.conicet.gov.ar:11336/257862instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:09:27.453CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Generalized inverses, ideals, and projectors in rings
title Generalized inverses, ideals, and projectors in rings
spellingShingle Generalized inverses, ideals, and projectors in rings
Morillas, Patricia Mariela
GENERALIZED INVERSE
RING
IDEAL
DIRECT SUM
PROJECTOR
INVOLUTION
title_short Generalized inverses, ideals, and projectors in rings
title_full Generalized inverses, ideals, and projectors in rings
title_fullStr Generalized inverses, ideals, and projectors in rings
title_full_unstemmed Generalized inverses, ideals, and projectors in rings
title_sort Generalized inverses, ideals, and projectors in rings
dc.creator.none.fl_str_mv Morillas, Patricia Mariela
author Morillas, Patricia Mariela
author_facet Morillas, Patricia Mariela
author_role author
dc.subject.none.fl_str_mv GENERALIZED INVERSE
RING
IDEAL
DIRECT SUM
PROJECTOR
INVOLUTION
topic GENERALIZED INVERSE
RING
IDEAL
DIRECT SUM
PROJECTOR
INVOLUTION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring R with a unit 1 , 0. We prove that generalized inverses in R are related to idempotent group endomorphisms ρ : R → R, called projectors. We use these relations to give characterizations and existence conditions for {1}, {2}, and {1, 2}-inverses with any given principal/annihilator ideals. As a consequence, we obtain sufficient conditions for any right/left ideal of R to be a principal or an annihilator ideal of an idempotent element of R. We also study some particular generalized inverses: Drazin and (b, c) inverses, and (e, f) Moore-Penrose, e-core, f-dual core, w-core, dual v-core, right w-core, left dual v-core, and (p, q) inverses in rings with involution.
Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
description The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring R with a unit 1 , 0. We prove that generalized inverses in R are related to idempotent group endomorphisms ρ : R → R, called projectors. We use these relations to give characterizations and existence conditions for {1}, {2}, and {1, 2}-inverses with any given principal/annihilator ideals. As a consequence, we obtain sufficient conditions for any right/left ideal of R to be a principal or an annihilator ideal of an idempotent element of R. We also study some particular generalized inverses: Drazin and (b, c) inverses, and (e, f) Moore-Penrose, e-core, f-dual core, w-core, dual v-core, right w-core, left dual v-core, and (p, q) inverses in rings with involution.
publishDate 2024
dc.date.none.fl_str_mv 2024-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/257862
Morillas, Patricia Mariela; Generalized inverses, ideals, and projectors in rings; University of Nis; Filomat; 38; 19; 4-2024; 6715-6741
0354-5180
CONICET Digital
CONICET
url http://hdl.handle.net/11336/257862
identifier_str_mv Morillas, Patricia Mariela; Generalized inverses, ideals, and projectors in rings; University of Nis; Filomat; 38; 19; 4-2024; 6715-6741
0354-5180
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.pmf.ni.ac.rs/filomat-content/2024/38-19/FILOMAT%2038-19.html
info:eu-repo/semantics/altIdentifier/url/https://www.pmf.ni.ac.rs/filomat-content/2024/38-19/38-19-7-22749.pdf
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/pdf/2304.06149
info:eu-repo/semantics/altIdentifier/doi/10.2298/FIL2419715M
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv University of Nis
publisher.none.fl_str_mv University of Nis
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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