A contramodule generalization of Neeman's flat and projective module theorem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00641196" target="_blank" >RIV/67985840:_____/25:00641196 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s40062-025-00378-5" target="_blank" >https://doi.org/10.1007/s40062-025-00378-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40062-025-00378-5" target="_blank" >10.1007/s40062-025-00378-5</a>
Alternative languages
Result language
angličtina
Original language name
A contramodule generalization of Neeman's flat and projective module theorem
Original language description
This paper builds on top of Positselski (J Homot Relat Struct 19(4):635-678, 2024). We consider a complete, separated topological ring R with a countable base of neighborhoods of zero consisting of open two-sided ideals. The main result is that the homotopy category of projective left R-contramodules is equivalent to the derived category of the exact category of flat left R-contramodules, and also to the homotopy category of flat cotorsion left R-contramodules. In other words, a complex of flat R-contramodules is contraacyclic (in the sense of Becker) if and only if it is an acyclic complex with flat R-contramodules of cocycles, and if and only if it is coacyclic as a complex in the exact category of flat R-contramodules. These are contramodule generalizations of theorems of Neeman and of Bazzoni, Cortés-Izurdiaga, and Estrada.
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/GA23-05148S" target="_blank" >GA23-05148S: Homological and structural theory in geometric contexts</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Homotopy and Related Structures
ISSN
2193-8407
e-ISSN
1512-2891
Volume of the periodical
20
Issue of the periodical within the volume
4
Country of publishing house
GE - GEORGIA
Number of pages
34
Pages from-to
477-510
UT code for WoS article
001530443300001
EID of the result in the Scopus database
2-s2.0-105010772089