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

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Skowroński A.

Open Mathematics

2003

tom 1

nr 1

108-122

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.

Ograniczanie wyników

1 Open Mathematics

1 Skowroński A.

1 2003

Wyniki wyszukiwania

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