An explicit self-dual construction of complete cotorsion pairs in the relative context

0571081 - MÚ 2024 RIV CH eng J - Článek v odborném periodiku
Positselski, Leonid
An explicit self-dual construction of complete cotorsion pairs in the relative context.
Rendiconti del Seminario Matematico della Universita di Padova. Roč. 149, č. 1 (2023), s. 191-253. ISSN 0041-8994. E-ISSN 2240-2926
Grant CEP: GA ČR(CZ) GA20-13778S
Institucionální podpora: RVO:67985840
Klíčová slova: filtrations and cofiltrations * induced and coinduced modules * n-tiling and n-cotilting modules
Obor OECD: Pure mathematics
Impakt faktor: 0.3, rok: 2022
Způsob publikování: Open access
https://doi.org/10.4171/rsmup/118

Let R → A be a map of associative rings, and let (F,C) be a hereditary complete cotorsion pair in R−Mod. Let (FA,CA) be the cotorsion pair in A−Mod in which FA is the class of all left A-modules whose underlying R-modules belong to F. Assuming that the F-resolution dimension of every left R-module is finite and the class F is preserved by the coinduction functor Hom⁡R(A,−), we show that CA is the class of all direct summands of left A-modules finitely (co)filtered by A-modules coinduced from R-modules from C. If the class F is closed under countable products and preserved by the functor Hom⁡R(A,−), we prove that CA​ is the class of all direct summands of left A-modules cofiltered by A-modules coinduced from R-modules from C, with the decreasing filtration indexed by the natural numbers. A combined result is also obtained. As an illustration of the main results of the paper, we consider certain cotorsion pairs related to the contraderived and coderived categories of curved DG-modules.
Trvalý link: https://hdl.handle.net/11104/0342386