Finitistic dimension conjectures via Gorenstein projective dimension

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Finitistic dimension conjectures via Gorenstein projective dimension

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Finitistic dimension conjectures via Gorenstein projective dimension

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-13778S" target="_blank" >GA20-13778S: Symetrie, duality a aproximace v derivované algebraické geometrii a teorii reprezentací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Algebra

ISSN

0021-8693

e-ISSN

1090-266X

Svazek periodika

591

Číslo periodika v rámci svazku

591

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

15-35

Kód UT WoS článku

000715378600002

EID výsledku v databázi Scopus

2-s2.0-85118506103