On artin algebras with almost all indecomposable modules of projective or injective dimension at most one

• Autorzy: Andrzej Skowroński
• Języki publikacji: EN

Abstrakty

EN

Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote $$\mathcal{L}_A$$ to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by $$\mathcal{R}_A$$ the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with $$\mathcal{L}_A \cup \mathcal{R}_A$$ co-finite in ind A, quasi-tilted algebras and generalized double tilted algebras, have been extensively investigated. The aim of the paper is to show that these two classes of algebras exhaust the class of all artin algebras A for which $$\mathcal{L}_A \cup \mathcal{R}_A$$ is co-finite in ind A, and derive some consequences.

Słowa kluczowe

EN

artin algebra; quasi-tilted algebra; generalized double tilted algebra; Auslander-Reiten quiver; projective dimension; injective dimension; Primary 16G70; 18G20; Secondary 16G10

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 1
• Strony: 108-122

Daty

wydano

2003-03-01

online

2003-03-01

Twórcy

autor

Andrzej Skowroński

• Nicolaus Copernicus University

Bibliografia

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Identyfikatory

DOI

10.2478/BF02475668