Approximation properties of torsion classes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10488360" target="_blank" >RIV/00216208:11320/24:10488360 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=q5KOyhmDQr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=q5KOyhmDQr</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.13169" target="_blank" >10.1112/blms.13169</a>

Result language
angličtina
Original language name
Approximation properties of torsion classes
Original language description
We strengthen a result of Bagaria and Magidor (Trans.Amer. Math. Soc. 366 (2014), no. 4, 1857-1877) about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the Maximum Deconstructibility principle introduced in Cox (J. Pure Appl. Algebra 226 (2022), no. 5) requires large cardinals; it sits, implication-wise, between Vopěnka's Principle and the existence of an ????1-strongly compact cardinal.(2) While deconstructibility of a class of modules always implies the precovering property by Saorín and Šťovíček (Adv. Math. 228 (2011), no. 2, 968-1007), the concepts are (consistently) nonequivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits
Czech name
—
Czech description
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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

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)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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