An explicit self-dual construction of complete cotorsion pairs in the relative context

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00571081" target="_blank" >RIV/67985840:_____/23:00571081 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4171/rsmup/118" target="_blank" >https://doi.org/10.4171/rsmup/118</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4171/RSMUP/118" target="_blank" >10.4171/RSMUP/118</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An explicit self-dual construction of complete cotorsion pairs in the relative context

Popis výsledku v původním jazyce

Let R → A be a map of associative rings, and let (F,C) be a hereditary complete cotorsion pair in R−Mod. Let (FA,CA) be the cotorsion pair in A−Mod in which FA is the class of all left A-modules whose underlying R-modules belong to F. Assuming that the F-resolution dimension of every left R-module is finite and the class F is preserved by the coinduction functor Hom⁡R(A,−), we show that CA is the class of all direct summands of left A-modules finitely (co)filtered by A-modules coinduced from R-modules from C. If the class F is closed under countable products and preserved by the functor Hom⁡R(A,−), we prove that CA​ is the class of all direct summands of left A-modules cofiltered by A-modules coinduced from R-modules from C, with the decreasing filtration indexed by the natural numbers. A combined result is also obtained. As an illustration of the main results of the paper, we consider certain cotorsion pairs related to the contraderived and coderived categories of curved DG-modules.

Název v anglickém jazyce

An explicit self-dual construction of complete cotorsion pairs in the relative context

Popis výsledku anglicky

Let R → A be a map of associative rings, and let (F,C) be a hereditary complete cotorsion pair in R−Mod. Let (FA,CA) be the cotorsion pair in A−Mod in which FA is the class of all left A-modules whose underlying R-modules belong to F. Assuming that the F-resolution dimension of every left R-module is finite and the class F is preserved by the coinduction functor Hom⁡R(A,−), we show that CA is the class of all direct summands of left A-modules finitely (co)filtered by A-modules coinduced from R-modules from C. If the class F is closed under countable products and preserved by the functor Hom⁡R(A,−), we prove that CA​ is the class of all direct summands of left A-modules cofiltered by A-modules coinduced from R-modules from C, with the decreasing filtration indexed by the natural numbers. A combined result is also obtained. As an illustration of the main results of the paper, we consider certain cotorsion pairs related to the contraderived and coderived categories of curved DG-modules.

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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Rendiconti del Seminario Matematico della Universita di Padova

ISSN

0041-8994

e-ISSN

2240-2926

Svazek periodika

149

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

63

Strana od-do

191-253

Kód UT WoS článku

000980736000008

EID výsledku v databázi Scopus

2-s2.0-85159139827