Generalized periodicity theorems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00618846" target="_blank" >RIV/67985840:_____/25:00618846 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jpaa.2025.107962" target="_blank" >https://doi.org/10.1016/j.jpaa.2025.107962</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2025.107962" target="_blank" >10.1016/j.jpaa.2025.107962</a>

Result language
angličtina
Original language name
Generalized periodicity theorems
Original language description
Let R be a ring and S be a class of strongly finitely presented (FP∞) R-modules closed under extensions, direct summands, and syzygies. Let (A,B) be the (hereditary complete) cotorsion pair generated by S in Mod-R, and let (C,D) be the (also hereditary complete) cotorsion pair in which C=lim→A=lim→S. We show that any A-periodic module in C belongs to A, and any D-periodic module in B belongs to D. Further generalizations of both results are obtained, so that we get a common generalization of the flat/projective and fp-projective periodicity theorems, as well as a common generalization of the fp-injective/injective and cotorsion periodicity theorems. Both are applicable to modules over an arbitrary ring, and in fact, to Grothendieck categories.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

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

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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