Enochs' conjecture for small precovering classes of modules
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471316" target="_blank" >RIV/00216208:11320/23:10471316 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=n~UmPujewz" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=n~UmPujewz</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-022-2421-4" target="_blank" >10.1007/s11856-022-2421-4</a>
Alternative languages
Result language
angličtina
Original language name
Enochs' conjecture for small precovering classes of modules
Original language description
Enochs' conjecture asserts that each covering class of modules (over any fixed 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 short paper, we prove the validity of the conjecture for small precovering classes, i.e., the classes of the form Add(M) where M is any module, under a mild additional set-theoretic assumption which ensures that there are enough non-reflecting stationary sets. We even show that M has a perfect decomposition if Add(M) is a covering class. Finally, the additional set-theoretic assumption is shown to be redundant if there exists an n < <omega> such that M decomposes into a direct sum of ?(n)-generated mo dules.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Israel Journal of Mathematics
ISSN
0021-2172
e-ISSN
1565-8511
Volume of the periodical
255
Issue of the periodical within the volume
1
Country of publishing house
IL - THE STATE OF ISRAEL
Number of pages
15
Pages from-to
401-415
UT code for WoS article
001034664500017
EID of the result in the Scopus database
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