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 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 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 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 is co-finite in ind A, and derive some consequences.
@article{bwmeta1.element.doi-10_2478_BF02475668,
author = {Andrzej Skowro\'nski},
title = {On artin algebras with almost all indecomposable modules of projective or injective dimension at most one},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {108-122},
zbl = {1035.16008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475668}
}
Andrzej Skowroński. On artin algebras with almost all indecomposable modules of projective or injective dimension at most one. Open Mathematics, Tome 1 (2003) pp. 108-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475668/
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