Topologically semisimple and topologically perfect topological rings

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00558266" target="_blank" >RIV/67985840:_____/22:00558266 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/22:10452304

Výsledek na webu

<a href="http://https:dx.doi.org/10.5565/PUBLMAT6622202" target="_blank" >http://https:dx.doi.org/10.5565/PUBLMAT6622202</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5565/PUBLMAT6622202" target="_blank" >10.5565/PUBLMAT6622202</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Topologically semisimple and topologically perfect topological rings

Popis výsledku v původním jazyce

Extending the Wedderburn-Artin theory of semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split (equivalently, semisimple) if and only if the abelian category of discrete right modules over the same ring is split (equivalently, semisimple). An extension of the Bass theory of left perfect rings to the topological realm is formulated as a list of conjecturally equivalent conditions, many equivalences and implications between which we prove. In particular, all the conditions are equivalent for topological rings with a countable base of neighborhoods of zero. We establish a connection between the concept of a topologically perfect topological ring and the theory of modules with perfect decomposition and show that a countably generated module Sigma-coperfect over its endomorphism ring has a perfect decomposition, partially answering a question of Angeleri Hugel and Saorin.

Název v anglickém jazyce

Topologically semisimple and topologically perfect topological rings

Popis výsledku anglicky

Extending the Wedderburn-Artin theory of semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split (equivalently, semisimple) if and only if the abelian category of discrete right modules over the same ring is split (equivalently, semisimple). An extension of the Bass theory of left perfect rings to the topological realm is formulated as a list of conjecturally equivalent conditions, many equivalences and implications between which we prove. In particular, all the conditions are equivalent for topological rings with a countable base of neighborhoods of zero. We establish a connection between the concept of a topologically perfect topological ring and the theory of modules with perfect decomposition and show that a countably generated module Sigma-coperfect over its endomorphism ring has a perfect decomposition, partially answering a question of Angeleri Hugel and Saorin.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-23112S" target="_blank" >GA17-23112S: Strukturní teorie reprezentací algeber (lokalizace a vychylující teorie)</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

Publicacions Matematiques

ISSN

0214-1493

e-ISSN

0214-1493

Svazek periodika

66

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

84

Strana od-do

457-540

Kód UT WoS článku

000830838900002

EID výsledku v databázi Scopus

2-s2.0-85133329381