Closure properties of lim⟶⁡C

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557710" target="_blank" >RIV/67985840:_____/22:00557710 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/22:10453364

Výsledek na webu

<a href="https://doi.org/10.1016/j.jalgebra.2022.04.029" target="_blank" >https://doi.org/10.1016/j.jalgebra.2022.04.029</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jalgebra.2022.04.029" target="_blank" >10.1016/j.jalgebra.2022.04.029</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Closure properties of lim⟶⁡C

Popis výsledku v původním jazyce

Let C be a class of modules and L = lim C the class of all direct limits of modules from C. The class L is well understood when C consists of finitely presented modules: L then enjoys various closure properties. We study the closure properties of L in the general case when C is arbitrary class of modules. Then we concentrate on two important particular cases, when C = add M and C = Add M, for an arbitrary module M. In the first case, we prove that L is the class of all tensor products of L with flat modules over the endomorphism ring of M. In the second case, we show that L is the class of all contratensor products of M, over the endomorphism ring of M endowed with the finite topology, with contramodules that can be obtained as direct limits of projective contramodules. For modules M from various classes of modules (e.g., for pure projective modules), we prove that lim add M = lim Add M, but the general case remains open.

Název v anglickém jazyce

Closure properties of lim⟶⁡C

Popis výsledku anglicky

Let C be a class of modules and L = lim C the class of all direct limits of modules from C. The class L is well understood when C consists of finitely presented modules: L then enjoys various closure properties. We study the closure properties of L in the general case when C is arbitrary class of modules. Then we concentrate on two important particular cases, when C = add M and C = Add M, for an arbitrary module M. In the first case, we prove that L is the class of all tensor products of L with flat modules over the endomorphism ring of M. In the second case, we show that L is the class of all contratensor products of M, over the endomorphism ring of M endowed with the finite topology, with contramodules that can be obtained as direct limits of projective contramodules. For modules M from various classes of modules (e.g., for pure projective modules), we prove that lim add M = lim Add M, but the general case remains open.

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

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

606

Číslo periodika v rámci svazku

September 15

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

74

Strana od-do

30-103

Kód UT WoS článku

000831078600003

EID výsledku v databázi Scopus

2-s2.0-85131374268