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Closure properties of lim⟶C
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SYSNO ASEP 0557710 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Closure properties of lim⟶C Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID
Příhoda, P. (CZ)
Trlifaj, J. (CZ)Source Title Journal of Algebra. - : Elsevier - ISSN 0021-8693
Roč. 606, September 15 (2022), s. 30-103Number of pages 74 s. Language eng - English Country US - United States Keywords direct limits in module categories ; pure projective modules ; flat contramodules over topological rings Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA20-13778S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000831078600003 EID SCOPUS 85131374268 DOI 10.1016/j.jalgebra.2022.04.029 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2023 Electronic address https://doi.org/10.1016/j.jalgebra.2022.04.029
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