Degrees of irreducible morphisms and finite-representation type

Autores
Chaio, Claudia Alicia; Le Meur, Patrick; Trepode, Sonia Elisabet
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree in terms of the existence of certain annihilator maps. This is used to prove our main theorem: An algebra is of finite representation type if and only if for every indecomposable projective the inclusion of the radical in the projective has finite right degree, which is equivalent to requiring that for every indecomposable injective the epimorphism from the injective to its quotient by its socle has finite left degree. As an application of the techniques we develop, we study the behavior of the composite of paths of irreducible morphisms between indecomposable modules.
Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Le Meur, Patrick. Universite Blaise Pascal; Francia
Fil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
DEGREES
COVERING
COMPOSITION
FINITE REPRESENTATION TYPE
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:11336/245636
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Degrees of irreducible morphisms and finite-representation typeChaio, Claudia AliciaLe Meur, PatrickTrepode, Sonia ElisabetDEGREESCOVERINGCOMPOSITIONFINITE REPRESENTATION TYPEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree in terms of the existence of certain annihilator maps. This is used to prove our main theorem: An algebra is of finite representation type if and only if for every indecomposable projective the inclusion of the radical in the projective has finite right degree, which is equivalent to requiring that for every indecomposable injective the epimorphism from the injective to its quotient by its socle has finite left degree. As an application of the techniques we develop, we study the behavior of the composite of paths of irreducible morphisms between indecomposable modules.Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Le Meur, Patrick. Universite Blaise Pascal; FranciaFil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaOxford University Press2011-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/245636Chaio, Claudia Alicia; Le Meur, Patrick; Trepode, Sonia Elisabet; Degrees of irreducible morphisms and finite-representation type; Oxford University Press; Journal of the London Mathematical Society; 84; 1; 8-2011; 35-570024-6107CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/jdq104info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdq104info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:25:57Zoai:ri.conicet.gov.ar:11336/245636instacron: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:34982025-11-05 10:25:57.387CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Degrees of irreducible morphisms and finite-representation type
title Degrees of irreducible morphisms and finite-representation type
spellingShingle Degrees of irreducible morphisms and finite-representation type
Chaio, Claudia Alicia
DEGREES
COVERING
COMPOSITION
FINITE REPRESENTATION TYPE
title_short Degrees of irreducible morphisms and finite-representation type
title_full Degrees of irreducible morphisms and finite-representation type
title_fullStr Degrees of irreducible morphisms and finite-representation type
title_full_unstemmed Degrees of irreducible morphisms and finite-representation type
title_sort Degrees of irreducible morphisms and finite-representation type
dc.creator.none.fl_str_mv Chaio, Claudia Alicia
Le Meur, Patrick
Trepode, Sonia Elisabet
author Chaio, Claudia Alicia
author_facet Chaio, Claudia Alicia
Le Meur, Patrick
Trepode, Sonia Elisabet
author_role author
author2 Le Meur, Patrick
Trepode, Sonia Elisabet
author2_role author
author
dc.subject.none.fl_str_mv DEGREES
COVERING
COMPOSITION
FINITE REPRESENTATION TYPE
topic DEGREES
COVERING
COMPOSITION
FINITE REPRESENTATION TYPE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree in terms of the existence of certain annihilator maps. This is used to prove our main theorem: An algebra is of finite representation type if and only if for every indecomposable projective the inclusion of the radical in the projective has finite right degree, which is equivalent to requiring that for every indecomposable injective the epimorphism from the injective to its quotient by its socle has finite left degree. As an application of the techniques we develop, we study the behavior of the composite of paths of irreducible morphisms between indecomposable modules.
Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Le Meur, Patrick. Universite Blaise Pascal; Francia
Fil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree in terms of the existence of certain annihilator maps. This is used to prove our main theorem: An algebra is of finite representation type if and only if for every indecomposable projective the inclusion of the radical in the projective has finite right degree, which is equivalent to requiring that for every indecomposable injective the epimorphism from the injective to its quotient by its socle has finite left degree. As an application of the techniques we develop, we study the behavior of the composite of paths of irreducible morphisms between indecomposable modules.
publishDate 2011
dc.date.none.fl_str_mv 2011-08
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/11336/245636
Chaio, Claudia Alicia; Le Meur, Patrick; Trepode, Sonia Elisabet; Degrees of irreducible morphisms and finite-representation type; Oxford University Press; Journal of the London Mathematical Society; 84; 1; 8-2011; 35-57
0024-6107
CONICET Digital
CONICET
url http://hdl.handle.net/11336/245636
identifier_str_mv Chaio, Claudia Alicia; Le Meur, Patrick; Trepode, Sonia Elisabet; Degrees of irreducible morphisms and finite-representation type; Oxford University Press; Journal of the London Mathematical Society; 84; 1; 8-2011; 35-57
0024-6107
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://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/jdq104
info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdq104
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
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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 13.084122

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