Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner

Autores
Fernández, Elsa Adriana; Platzeck, Maria Ines
Año de publicación
2002
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. We describe the ordinary quiver and relations for T(Λ) = Λ ⋉ D(Λ), the trivial extension of Λ by its minimal injective cogenerator D(Λ), and also for the repetitive algebra Λ of Λ. Associated with this description we give an application of a theorem of Sheila Brenner.
Fil: Fernández, Elsa Adriana. Universidad Nacional de la Patagonia. Facultad de Ingeniería. Sede Puerto Madryn; 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
Materia
Modules
Artin Algebras
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/78775
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila BrennerFernández, Elsa AdrianaPlatzeck, Maria InesModulesArtin Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. We describe the ordinary quiver and relations for T(Λ) = Λ ⋉ D(Λ), the trivial extension of Λ by its minimal injective cogenerator D(Λ), and also for the repetitive algebra Λ of Λ. Associated with this description we give an application of a theorem of Sheila Brenner.Fil: Fernández, Elsa Adriana. Universidad Nacional de la Patagonia. Facultad de Ingeniería. Sede Puerto Madryn; 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; ArgentinaAcademic Press Inc Elsevier Science2002-03-15info: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/11336/78775Fernández, Elsa Adriana; Platzeck, Maria Ines; Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner; Academic Press Inc Elsevier Science; Journal of Algebra; 249; 2; 15-3-2002; 326-3440021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869301990568info:eu-repo/semantics/altIdentifier/doi/10.1006/jabr.2001.9056info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:30:48Zoai:ri.conicet.gov.ar:11336/78775instacron: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 11:30:49.036CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
title Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
spellingShingle Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
Fernández, Elsa Adriana
Modules
Artin Algebras
title_short Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
title_full Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
title_fullStr Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
title_full_unstemmed Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
title_sort Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner
dc.creator.none.fl_str_mv Fernández, Elsa Adriana
Platzeck, Maria Ines
author Fernández, Elsa Adriana
author_facet Fernández, Elsa Adriana
Platzeck, Maria Ines
author_role author
author2 Platzeck, Maria Ines
author2_role author
dc.subject.none.fl_str_mv Modules
Artin Algebras
topic Modules
Artin Algebras
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. We describe the ordinary quiver and relations for T(Λ) = Λ ⋉ D(Λ), the trivial extension of Λ by its minimal injective cogenerator D(Λ), and also for the repetitive algebra Λ of Λ. Associated with this description we give an application of a theorem of Sheila Brenner.
Fil: Fernández, Elsa Adriana. Universidad Nacional de la Patagonia. Facultad de Ingeniería. Sede Puerto Madryn; 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
description Let Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. We describe the ordinary quiver and relations for T(Λ) = Λ ⋉ D(Λ), the trivial extension of Λ by its minimal injective cogenerator D(Λ), and also for the repetitive algebra Λ of Λ. Associated with this description we give an application of a theorem of Sheila Brenner.
publishDate 2002
dc.date.none.fl_str_mv 2002-03-15
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/11336/78775
Fernández, Elsa Adriana; Platzeck, Maria Ines; Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner; Academic Press Inc Elsevier Science; Journal of Algebra; 249; 2; 15-3-2002; 326-344
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/78775
identifier_str_mv Fernández, Elsa Adriana; Platzeck, Maria Ines; Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner; Academic Press Inc Elsevier Science; Journal of Algebra; 249; 2; 15-3-2002; 326-344
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/S0021869301990568
info:eu-repo/semantics/altIdentifier/doi/10.1006/jabr.2001.9056
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv 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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