On the degree of irreducible morphisms

Autores
Chaio, Claudia Alicia; Platzeck, Maria Ines; Trepode, Sonia Elisabet
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the degree of irreducible morphisms in generalized standard convex components of the Auslander-Reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length. We call the components with this last property components with length. In particular, we give two criteria to determine wether the degree of such an irreducible morphism f is finite or infinite. One of them is given in terms of the compositions of f with non-zero maps between modules in the component. The other states that the left degree of an irreducible map f is finite if and only if Kerf belongs to the component. We apply our results to irreducible morphisms over artin algebras of finite representation type and over tame hereditary algebras.
Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Platzeck, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
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:11336/96029
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the degree of irreducible morphismsChaio, Claudia AliciaPlatzeck, Maria InesTrepode, Sonia Elisabethttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the degree of irreducible morphisms in generalized standard convex components of the Auslander-Reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length. We call the components with this last property components with length. In particular, we give two criteria to determine wether the degree of such an irreducible morphism f is finite or infinite. One of them is given in terms of the compositions of f with non-zero maps between modules in the component. The other states that the left degree of an irreducible map f is finite if and only if Kerf belongs to the component. We apply our results to irreducible morphisms over artin algebras of finite representation type and over tame hereditary algebras.Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Platzeck, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaAcademic Press Inc Elsevier Science2004-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/96029Chaio, Claudia Alicia; Platzeck, Maria Ines; Trepode, Sonia Elisabet; On the degree of irreducible morphisms; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 1; 11-2004; 200-2240021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2004.06.024info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869304003503info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:15:30Zoai:ri.conicet.gov.ar:11336/96029instacron: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:34982025-10-22 12:15:30.893CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the degree of irreducible morphisms
title On the degree of irreducible morphisms
spellingShingle On the degree of irreducible morphisms
Chaio, Claudia Alicia
title_short On the degree of irreducible morphisms
title_full On the degree of irreducible morphisms
title_fullStr On the degree of irreducible morphisms
title_full_unstemmed On the degree of irreducible morphisms
title_sort On the degree of irreducible morphisms
dc.creator.none.fl_str_mv Chaio, Claudia Alicia
Platzeck, Maria Ines
Trepode, Sonia Elisabet
author Chaio, Claudia Alicia
author_facet Chaio, Claudia Alicia
Platzeck, Maria Ines
Trepode, Sonia Elisabet
author_role author
author2 Platzeck, Maria Ines
Trepode, Sonia Elisabet
author2_role author
author
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 generalized standard convex components of the Auslander-Reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length. We call the components with this last property components with length. In particular, we give two criteria to determine wether the degree of such an irreducible morphism f is finite or infinite. One of them is given in terms of the compositions of f with non-zero maps between modules in the component. The other states that the left degree of an irreducible map f is finite if and only if Kerf belongs to the component. We apply our results to irreducible morphisms over artin algebras of finite representation type and over tame hereditary algebras.
Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Platzeck, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description We study the degree of irreducible morphisms in generalized standard convex components of the Auslander-Reiten quiver of an artin algebra with the property that paths with the same origin and end vertices have equal length. We call the components with this last property components with length. In particular, we give two criteria to determine wether the degree of such an irreducible morphism f is finite or infinite. One of them is given in terms of the compositions of f with non-zero maps between modules in the component. The other states that the left degree of an irreducible map f is finite if and only if Kerf belongs to the component. We apply our results to irreducible morphisms over artin algebras of finite representation type and over tame hereditary algebras.
publishDate 2004
dc.date.none.fl_str_mv 2004-11
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/11336/96029
Chaio, Claudia Alicia; Platzeck, Maria Ines; Trepode, Sonia Elisabet; On the degree of irreducible morphisms; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 1; 11-2004; 200-224
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/96029
identifier_str_mv Chaio, Claudia Alicia; Platzeck, Maria Ines; Trepode, Sonia Elisabet; On the degree of irreducible morphisms; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 1; 11-2004; 200-224
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2004.06.024
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869304003503
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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 12.982451

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