Geodesic
Existence of cycle-finite algebras of infinite representation type without directing projective or injective modules
Piotr Malicki 1   ; José Antonio de la Peña 2   ; Andrzej Skowroński 1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Centro de Investigación en Matemáticas (CIMAT) Guanajuato, México
Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 165-190 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We solve an open problem concerning the existence of cycle-finite algebras of infinite representation type for which all indecomposable projective modules and indecomposable injective modules are nondirecting (lie on oriented cycles of indecomposable modules). We prove that there exist such algebras having large numbers of almost acyclic Auslander–Reiten components with finite cyclic multisections.
DOI : 10.4064/cm7190-2-2017
Keywords: solve problem concerning existence cycle finite algebras infinite representation type which indecomposable projective modules indecomposable injective modules nondirecting lie oriented cycles indecomposable modules prove there exist algebras having large numbers almost acyclic auslander reiten components finite cyclic multisections

Piotr Malicki  1   ; José Antonio de la Peña  2   ; Andrzej Skowroński  1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Centro de Investigación en Matemáticas (CIMAT) Guanajuato, México 
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Piotr Malicki; José Antonio de la Peña; Andrzej Skowroński. Existence of cycle-finite algebras of infinite representation type without directing projective or injective modules. Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 165-190. doi: 10.4064/cm7190-2-2017

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