Topologically semisimple and topologically perfect topological rings
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216208:11320/22:10452304
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Topologically semisimple and topologically perfect topological rings
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-23112S" target="_blank" >GA17-23112S: Structure theory for representations of algebras (localization and tilting theory)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Publicacions Matematiques
ISSN
0214-1493
e-ISSN
0214-1493
Volume of the periodical
66
Issue of the periodical within the volume
2
Country of publishing house
ES - SPAIN
Number of pages
84
Pages from-to
457-540
UT code for WoS article
000830838900002
EID of the result in the Scopus database
2-s2.0-85133329381