Enochs' conjecture for cotorsion pairs and more
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10488418" target="_blank" >RIV/00216208:11320/24:10488418 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=3Qd8ox_-R-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=3Qd8ox_-R-</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/forum-2023-0220" target="_blank" >10.1515/forum-2023-0220</a>
Alternative languages
Result language
angličtina
Original language name
Enochs' conjecture for cotorsion pairs and more
Original language description
Enochs' conjecture asserts that each covering class of modules (over any ring) has to be closed under direct limits. Although various special cases of the conjecture have been verified, the conjecture remains open in its full generality. In this paper, we prove the conjecture for the classes Filt (delta) , where delta consists of N-n-presented modules for some fixed n < omega. In particular, this applies to the left-hand class of any cotorsion pair generated by a class of N-n-presented modules. Moreover, we also show that it is consistent with ZFC that Enochs' conjecture holds for all classes of the form Filt (delta) , where delta is a set of modules. This leaves us with no explicit example of a covering class where we cannot prove that Enochs' conjecture holds (possibly under some additional set-theoretic assumption).
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/GA23-05148S" target="_blank" >GA23-05148S: Homological and structural theory in geometric contexts</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Forum Mathematicum
ISSN
0933-7741
e-ISSN
1435-5337
Volume of the periodical
36
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
12
Pages from-to
1517-1528
UT code for WoS article
001134560600001
EID of the result in the Scopus database
2-s2.0-85181494556