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dc.contributor.author
Chaio, Claudia Alicia
dc.date.available
2018-07-04T15:14:11Z
dc.date.issued
2015-09
dc.identifier.citation
Chaio, Claudia Alicia; Degrees in Auslander-Reiten components with almost split sequences of at most two middle terms; World Scientific; Journal of Algebra and its Applications; 14; 7; 9-2015; 1-27
dc.identifier.issn
0219-4988
dc.identifier.uri
http://hdl.handle.net/11336/51167
dc.description.abstract
We consider A to be an artin algebra. We study the degrees of irreducible morphisms between modules in Auslander-Reiten components Gamma having only almost split sequences with at most two indecomposable middle terms, that is, alpha(Gamma) leq 2. We prove that if f:X rightarrow Y is an irreducible epimorphism of finite left degree with X or Y indecomposable, then there exists a module Z in Gamma and a morphism varphi in Re^{n}(Z,X) and not in Re^{n+1}(Z,X) for some positive integer n such that f varphi=0. In particular, for such components if A is a finite dimensional algebra over an algebraically closed field and f=(f_1,f_2)^t:X rightarrow Y_1 oplus Y_2 is an irreducible morphism then we show that d_l(f)=d_l(f_1)+ d_l(f_2). We also characterize the artin algebras of finite representation type with alpha(Gamma_A) leq 2 in terms of a finite number of irreducible morphisms with finite degree.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
World Scientific
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Irreducible Morphisms
dc.subject
Representation Type
dc.subject
Degrees
dc.subject
Auslander-Reiten Quiver
dc.subject
Radical
dc.subject
Degrees
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Degrees in Auslander-Reiten components with almost split sequences of at most two middle terms
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-06-29T13:09:58Z
dc.journal.volume
14
dc.journal.number
7
dc.journal.pagination
1-27
dc.journal.pais
Singapur
dc.description.fil
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; Argentina
dc.journal.title
Journal of Algebra and its Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1142/S0219498815501066
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0219498815501066
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