Generalized coil enlargements of algebras

Skowroński

2005

Journal of Algebra

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We prove that the class of Artin algebras whose Auslander-Reiten quiver admits a separating family of almost cyclic coherent components coincides with the class of generalized multicoil enlargements of concealed canonical algebras. Moreover, the module category, homological properties and the representation type of Artin algebras with separating families of almost cyclic coherent Auslander-Reiten components are described.

Section: Lemma 36 γ Is a Generalized Standard Family Of Components mentioning

confidence: 99%

Algebras with separating almost cyclic coherent Auslander–Reiten components

Skowroński

2005

Journal of Algebra

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“…If s = 1, such a translation quiver Γ is said to be a generalized coil. The admissible operations of types (ad 1), (ad 2), (ad 3), (ad 1 * ), (ad 2 * ) and (ad 3 * ) have been introduced in [4,5], and the admissible operations (ad 4) and (ad 4 * ) for r = 0 in [18].…”

Section: Generalized Multicoilsmentioning

confidence: 99%

Degenerations for indecomposable modules in almost cyclic coherent Auslander–Reiten components

Journal of Pure and Applied Algebra

2010

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“…If s = 1, such a translation quiver Γ is said to be a generalized coil. The admissible operations of types (ad 1), (ad 2), (ad 3), (ad 1 * ), (ad 2 * ) and (ad 3 * ) have been introduced in [1][2][3], and the admissible operations (ad 4) and (ad 4 * ) for r = 0 in [17]. We refer also to [20] for the structure of indecomposable modules lying in (generalized) standard coils.…”

Section: Generalized Multicoil Enlargements Of Concealed Canonical Almentioning

confidence: 99%

On the composition factors of indecomposable modules in almost cyclic coherent Auslander–Reiten components

Journal of Pure and Applied Algebra

2006

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We prove that the indecomposable modules without selfextensions in generalized standard almost cyclic coherent Auslander-Reiten components without external short paths of artin algebra are uniquely determined by their composition factors. Moreover, we prove that there is a common bound on the numbers of indecomposable modules with the same composition factors lying in a generalized standard almost cyclic coherent Auslander-Reiten component without external short paths of artin algebra.