Covers and direct limits: A contramodule-based approach
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00545496" target="_blank" >RIV/67985840:_____/21:00545496 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00209-020-02654-x" target="_blank" >https://doi.org/10.1007/s00209-020-02654-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00209-020-02654-x" target="_blank" >10.1007/s00209-020-02654-x</a>
Alternative languages
Result language
angličtina
Original language name
Covers and direct limits: A contramodule-based approach
Original language description
We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits. In the n-tilting–cotilting correspondence context, if A is a Grothendieck abelian category and the related abelian category B is equivalent to the category of contramodules over a topological ring R belonging to one of certain four classes of topological rings (e. g., R is commutative), then the left tilting class is covering in A if and only if it is closed under direct limits in A, and if and only if all the discrete quotient rings of the topological ring R are perfect. Generally, if M is a module satisfying a certain telescope Hom exactness condition (e. g., M is Σ-pure-Ext^1-self-orthogonal) and the topological ring R of endomorphisms of M belongs to one of some seven classes of topological rings, then the class Add(M) is closed under direct limits if and only if every countable direct limit of copies of M has an Add(M)-cover, and if and only if M has perfect decomposition.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Zeitschrift
ISSN
0025-5874
e-ISSN
1432-1823
Volume of the periodical
299
Issue of the periodical within the volume
1-2
Country of publishing house
DE - GERMANY
Number of pages
52
Pages from-to
1-52
UT code for WoS article
000606276500003
EID of the result in the Scopus database
2-s2.0-85099087975