Closure properties of lim⟶C
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557710" target="_blank" >RIV/67985840:_____/22:00557710 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10453364
Result on the web
<a href="https://doi.org/10.1016/j.jalgebra.2022.04.029" target="_blank" >https://doi.org/10.1016/j.jalgebra.2022.04.029</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2022.04.029" target="_blank" >10.1016/j.jalgebra.2022.04.029</a>
Alternative languages
Result language
angličtina
Original language name
Closure properties of lim⟶C
Original language description
Let C be a class of modules and L = lim C the class of all direct limits of modules from C. The class L is well understood when C consists of finitely presented modules: L then enjoys various closure properties. We study the closure properties of L in the general case when C is arbitrary class of modules. Then we concentrate on two important particular cases, when C = add M and C = Add M, for an arbitrary module M. In the first case, we prove that L is the class of all tensor products of L with flat modules over the endomorphism ring of M. In the second case, we show that L is the class of all contratensor products of M, over the endomorphism ring of M endowed with the finite topology, with contramodules that can be obtained as direct limits of projective contramodules. For modules M from various classes of modules (e.g., for pure projective modules), we prove that lim add M = lim Add M, but the general case remains open.
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/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
2022
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 Algebra
ISSN
0021-8693
e-ISSN
1090-266X
Volume of the periodical
606
Issue of the periodical within the volume
September 15
Country of publishing house
US - UNITED STATES
Number of pages
74
Pages from-to
30-103
UT code for WoS article
000831078600003
EID of the result in the Scopus database
2-s2.0-85131374268