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

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Central European Journal of Mathematics

Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    Andrzej Skowroński

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  1. Andrzej Skowroński
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Dedicated to Stanislaw Balcerzyk on the occation of his 70th birthday

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Skowroński, A. On artin algebras with almost all indecomposable modules of projective or injective dimension at most one. centr.eur.j.math. 1, 108–122 (2003). https://doi.org/10.2478/BF02475668

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  • DOI: https://doi.org/10.2478/BF02475668

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