Flat ring epimorphisms of countable type

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00523855" target="_blank" >RIV/67985840:_____/20:00523855 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/S001708951900017X" target="_blank" >https://doi.org/10.1017/S001708951900017X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S001708951900017X" target="_blank" >10.1017/S001708951900017X</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Flat ring epimorphisms of countable type

Popis výsledku v původním jazyce

Let R → U be an associative ring epimorphism such that U is a flat left R-module. Assume that the related Gabriel topology of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1. Furthermore, the abelian category of left contramodules over the completion of R at fully faithfully embeds into the Geigle-Lenzing right perpendicular subcategory to U in the category of left R-modules, and every object of the latter abelian category is an extension of two objects of the former one. We discuss conditions under which the two abelian categories are equivalent. Given a right linear topology on an associative ring R, we consider the induced topology on every left R-module and, for a perfect Gabriel topology, compare the completion of a module with an appropriate Ext module. Finally, we characterize the U-strongly flat left R-modules by the two conditions of left positive-degree Ext-orthogonality to all left U-modules and all -separated -complete left R-modules.

Název v anglickém jazyce

Flat ring epimorphisms of countable type

Popis výsledku anglicky

Let R → U be an associative ring epimorphism such that U is a flat left R-module. Assume that the related Gabriel topology of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1. Furthermore, the abelian category of left contramodules over the completion of R at fully faithfully embeds into the Geigle-Lenzing right perpendicular subcategory to U in the category of left R-modules, and every object of the latter abelian category is an extension of two objects of the former one. We discuss conditions under which the two abelian categories are equivalent. Given a right linear topology on an associative ring R, we consider the induced topology on every left R-module and, for a perfect Gabriel topology, compare the completion of a module with an appropriate Ext module. Finally, we characterize the U-strongly flat left R-modules by the two conditions of left positive-degree Ext-orthogonality to all left U-modules and all -separated -complete left R-modules.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Glasgow Mathematical Journal

ISSN

0017-0895

e-ISSN

—

Svazek periodika

62

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

57

Strana od-do

383-439

Kód UT WoS článku

000525379300008

EID výsledku v databázi Scopus

2-s2.0-85065401417