Projective covers of flat contramodules
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00565896" target="_blank" >RIV/67985840:_____/22:00565896 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10452390
Result on the web
<a href="https://doi.org/10.1093/imrn/rnab202" target="_blank" >https://doi.org/10.1093/imrn/rnab202</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnab202" target="_blank" >10.1093/imrn/rnab202</a>
Alternative languages
Result language
angličtina
Original language name
Projective covers of flat contramodules
Original language description
We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for infinity-strictly flat contramodules of projective dimension not exceeding 1, using an argument based on the notion of the topological Jacobson radical. Covers and precovers of direct limits of more general classes of objects, both in abelian categories with exact and with nonexact direct limits, are also discussed, with an eye towards the Enochs conjecture about covers and direct limits, using locally split (mono)morphisms as the main technique. In particular, we offer a simple elementary proof of the Enochs conjecture for the left class of an n-tilting cotorsion pair in an abelian category with exact direct limits.
Czech name
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Czech description
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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
International Mathematics Research Notices
ISSN
1073-7928
e-ISSN
1687-0247
Volume of the periodical
2022
Issue of the periodical within the volume
24
Country of publishing house
US - UNITED STATES
Number of pages
38
Pages from-to
19527-19564
UT code for WoS article
000790069800001
EID of the result in the Scopus database
2-s2.0-85118708770