Finitistic dimension conjectures via Gorenstein projective dimension
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452290" target="_blank" >RIV/00216208:11320/22:10452290 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FaU85WcU1D" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FaU85WcU1D</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2021.10.026" target="_blank" >10.1016/j.jalgebra.2021.10.026</a>
Alternative languages
Result language
angličtina
Original language name
Finitistic dimension conjectures via Gorenstein projective dimension
Original language description
It is a well-known result of Auslander and Reiten that contravariant finiteness of the class P-infinity(fin)( of finitely generated modules of finite projective dimension) over an Artin algebra is a sufficient condition for validity of finitistic dimension conjectures. Motivated by the fact that finitistic dimensions of an algebra can alternatively be computed by Gorenstein projective dimension, we examine in this work the Gorenstein counterpart of Auslander-Reiten condition, namely contravariant finiteness of the class GP(infinity)(fin) (of finitely generated modules of finite Gorenstein projective dimension), and its relation to validity of finitistic dimension conjectures. It is proved that contravariant finiteness of the class GP(infinity)(fin) implies validity of the second finitistic dimension conjecture over left artinian rings. In the more special setting of Artin algebras, however, it is proved that the Auslander-Reiten sufficient condition and its Gorenstein counterpart are virtually equivalent in the sense that contravariant finiteness of the class GP(infinity)(fin) implies contravariant finiteness of the class P-infinity(fin) over any Artin algebra, and the converse holds for Artin algebras over which the class GP(0)(fin) (of finitely generated Gorenstein projective modules) is contravariantly finite. (c) 2021 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Algebra
ISSN
0021-8693
e-ISSN
1090-266X
Volume of the periodical
591
Issue of the periodical within the volume
591
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
15-35
UT code for WoS article
000715378600002
EID of the result in the Scopus database
2-s2.0-85118506103