Contramodules over pro-perfect topological rings

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00551157" target="_blank" >RIV/67985840:_____/22:00551157 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1515/forum-2021-0010" target="_blank" >https://doi.org/10.1515/forum-2021-0010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/forum-2021-0010" target="_blank" >10.1515/forum-2021-0010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Contramodules over pro-perfect topological rings

Popis výsledku v původním jazyce

For four wide classes of topological rings R, we show that all flat left R-contramodules have projective covers if and only if all flat left R-contramodules are projective if and only if all left R-contramodules have projective covers if and only if all descending chains of cyclic discrete right R-modules terminate if and only if all the discrete quotient rings of R are left perfect. Three classes of topological rings for which this holds are the complete, separated topological associative rings with a base of neighborhoods of zero formed by open two-sided ideals such that either the ring is commutative, or it has a countable base of neighborhoods of zero, or it has only a finite number of semisimple discrete quotient rings. The fourth class consists of some topological rings with a base of open right ideals, it is a generalization of the first three classes. The key technique on which the proofs are based is the contramodule Nakayama lemma for topologically T-nilpotent ideals.

Název v anglickém jazyce

Contramodules over pro-perfect topological rings

Popis výsledku anglicky

For four wide classes of topological rings R, we show that all flat left R-contramodules have projective covers if and only if all flat left R-contramodules are projective if and only if all left R-contramodules have projective covers if and only if all descending chains of cyclic discrete right R-modules terminate if and only if all the discrete quotient rings of R are left perfect. Three classes of topological rings for which this holds are the complete, separated topological associative rings with a base of neighborhoods of zero formed by open two-sided ideals such that either the ring is commutative, or it has a countable base of neighborhoods of zero, or it has only a finite number of semisimple discrete quotient rings. The fourth class consists of some topological rings with a base of open right ideals, it is a generalization of the first three classes. The key technique on which the proofs are based is the contramodule Nakayama lemma for topologically T-nilpotent ideals.

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

Forum Mathematicum

ISSN

0933-7741

e-ISSN

1435-5337

Svazek periodika

34

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

39

Strana od-do

1-39

Kód UT WoS článku

000737425500001

EID výsledku v databázi Scopus

2-s2.0-85120616208