The composite of irreducible morphisms in standard components

Autores
Chaio, Claudia Alicia; Trepode, Sonia Elisabet
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, we consider standard components of the Auslander– Reiten quiver with trivial valuation. We give a characterization of when there are n irreducible morphisms between modules in such a component with non-zero composite belonging to the n + 1-th power of the radical. We prove that a necessary condition for their existence is that it has to be a non-zero cycle or a non-zero bypass in the component. For directed algebras, we prove that the composite of n irreducible morphisms between indecomposable modules belongs to a greater power of the radical, greater than n, if and only if it is zero.
Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Trepode, Sonia Elisabet. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Materia
universal covering
standard component
irreducible morphism
radical
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:11336/242753
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/242753
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The composite of irreducible morphisms in standard componentsChaio, Claudia AliciaTrepode, Sonia Elisabetuniversal coveringstandard componentirreducible morphismradicalhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work, we consider standard components of the Auslander– Reiten quiver with trivial valuation. We give a characterization of when there are n irreducible morphisms between modules in such a component with non-zero composite belonging to the n + 1-th power of the radical. We prove that a necessary condition for their existence is that it has to be a non-zero cycle or a non-zero bypass in the component. For directed algebras, we prove that the composite of n irreducible morphisms between indecomposable modules belongs to a greater power of the radical, greater than n, if and only if it is zero.Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Trepode, Sonia Elisabet. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaAcademic Press Inc Elsevier Science2010-02info: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/11336/242753Chaio, Claudia Alicia; Trepode, Sonia Elisabet; The composite of irreducible morphisms in standard components; Academic Press Inc Elsevier Science; Journal of Algebra; 323; 4; 2-2010; 1000-10110021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869309006322info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2009.11.022info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:36:14Zoai:ri.conicet.gov.ar:11336/242753instacron: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 09:36:15.022CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The composite of irreducible morphisms in standard components
title The composite of irreducible morphisms in standard components
spellingShingle The composite of irreducible morphisms in standard components
Chaio, Claudia Alicia
universal covering
standard component
irreducible morphism
radical
title_short The composite of irreducible morphisms in standard components
title_full The composite of irreducible morphisms in standard components
title_fullStr The composite of irreducible morphisms in standard components
title_full_unstemmed The composite of irreducible morphisms in standard components
title_sort The composite of irreducible morphisms in standard components
dc.creator.none.fl_str_mv Chaio, Claudia Alicia
Trepode, Sonia Elisabet
author Chaio, Claudia Alicia
author_facet Chaio, Claudia Alicia
Trepode, Sonia Elisabet
author_role author
author2 Trepode, Sonia Elisabet
author2_role author
dc.subject.none.fl_str_mv universal covering
standard component
irreducible morphism
radical
topic universal covering
standard component
irreducible morphism
radical
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work, we consider standard components of the Auslander– Reiten quiver with trivial valuation. We give a characterization of when there are n irreducible morphisms between modules in such a component with non-zero composite belonging to the n + 1-th power of the radical. We prove that a necessary condition for their existence is that it has to be a non-zero cycle or a non-zero bypass in the component. For directed algebras, we prove that the composite of n irreducible morphisms between indecomposable modules belongs to a greater power of the radical, greater than n, if and only if it is zero.
Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Trepode, Sonia Elisabet. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
description In this work, we consider standard components of the Auslander– Reiten quiver with trivial valuation. We give a characterization of when there are n irreducible morphisms between modules in such a component with non-zero composite belonging to the n + 1-th power of the radical. We prove that a necessary condition for their existence is that it has to be a non-zero cycle or a non-zero bypass in the component. For directed algebras, we prove that the composite of n irreducible morphisms between indecomposable modules belongs to a greater power of the radical, greater than n, if and only if it is zero.
publishDate 2010
dc.date.none.fl_str_mv 2010-02
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/11336/242753
Chaio, Claudia Alicia; Trepode, Sonia Elisabet; The composite of irreducible morphisms in standard components; Academic Press Inc Elsevier Science; Journal of Algebra; 323; 4; 2-2010; 1000-1011
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/242753
identifier_str_mv Chaio, Claudia Alicia; Trepode, Sonia Elisabet; The composite of irreducible morphisms in standard components; Academic Press Inc Elsevier Science; Journal of Algebra; 323; 4; 2-2010; 1000-1011
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/url/https://www.sciencedirect.com/science/article/pii/S0021869309006322
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2009.11.022
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 13.082534

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