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An explicit self-dual construction of complete cotorsion pairs in the relative context
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SYSNO ASEP 0571081 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název An explicit self-dual construction of complete cotorsion pairs in the relative context Tvůrce(i) Positselski, Leonid (MU-W) SAI, ORCID, RID Zdroj.dok. Rendiconti del Seminario Matematico della Universita di Padova. - : EMS Press - ISSN 0041-8994
Roč. 149, č. 1 (2023), s. 191-253Poč.str. 63 s. Jazyk dok. eng - angličtina Země vyd. CH - Švýcarsko Klíč. slova filtrations and cofiltrations ; induced and coinduced modules ; n-tiling and n-cotilting modules Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA20-13778S GA ČR - Grantová agentura ČR Způsob publikování Open access Institucionální podpora MU-W - RVO:67985840 UT WOS 000980736000008 EID SCOPUS 85159139827 DOI 10.4171/RSMUP/118 Anotace 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 HomR(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 HomR(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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2024 Elektronická adresa https://doi.org/10.4171/rsmup/118
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