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

Open Mathematics (2003)

- Volume: 1, Issue: 1, page 108-122
- ISSN: 2391-5455

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topAndrzej Skowroński. "On artin algebras with almost all indecomposable modules of projective or injective dimension at most one." Open Mathematics 1.1 (2003): 108-122. <http://eudml.org/doc/268914>.

@article{AndrzejSkowroński2003,

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.},

author = {Andrzej Skowroński},

journal = {Open Mathematics},

keywords = {Primary 16G70; 18G20; Secondary 16G10},

language = {eng},

number = {1},

pages = {108-122},

title = {On artin algebras with almost all indecomposable modules of projective or injective dimension at most one},

url = {http://eudml.org/doc/268914},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Andrzej Skowroński

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

JO - Open Mathematics

PY - 2003

VL - 1

IS - 1

SP - 108

EP - 122

AB - 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.

LA - eng

KW - Primary 16G70; 18G20; Secondary 16G10

UR - http://eudml.org/doc/268914

ER -

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