Covers and direct limits: A contramodule-based approach

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00545496" target="_blank" >RIV/67985840:_____/21:00545496 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00209-020-02654-x" target="_blank" >https://doi.org/10.1007/s00209-020-02654-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00209-020-02654-x" target="_blank" >10.1007/s00209-020-02654-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Covers and direct limits: A contramodule-based approach

Popis výsledku v původním jazyce

We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits. In the n-tilting–cotilting correspondence context, if A is a Grothendieck abelian category and the related abelian category B is equivalent to the category of contramodules over a topological ring R belonging to one of certain four classes of topological rings (e. g., R is commutative), then the left tilting class is covering in A if and only if it is closed under direct limits in A, and if and only if all the discrete quotient rings of the topological ring R are perfect. Generally, if M is a module satisfying a certain telescope Hom exactness condition (e. g., M is Σ-pure-Ext^1-self-orthogonal) and the topological ring R of endomorphisms of M belongs to one of some seven classes of topological rings, then the class Add(M) is closed under direct limits if and only if every countable direct limit of copies of M has an Add(M)-cover, and if and only if M has perfect decomposition.

Název v anglickém jazyce

Covers and direct limits: A contramodule-based approach

Popis výsledku anglicky

We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits. In the n-tilting–cotilting correspondence context, if A is a Grothendieck abelian category and the related abelian category B is equivalent to the category of contramodules over a topological ring R belonging to one of certain four classes of topological rings (e. g., R is commutative), then the left tilting class is covering in A if and only if it is closed under direct limits in A, and if and only if all the discrete quotient rings of the topological ring R are perfect. Generally, if M is a module satisfying a certain telescope Hom exactness condition (e. g., M is Σ-pure-Ext^1-self-orthogonal) and the topological ring R of endomorphisms of M belongs to one of some seven classes of topological rings, then the class Add(M) is closed under direct limits if and only if every countable direct limit of copies of M has an Add(M)-cover, and if and only if M has perfect decomposition.

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

2021

Kód důvěrnosti údajů

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

Název periodika

Mathematische Zeitschrift

ISSN

0025-5874

e-ISSN

1432-1823

Svazek periodika

299

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

52

Strana od-do

1-52

Kód UT WoS článku

000606276500003

EID výsledku v databázi Scopus

2-s2.0-85099087975