Projective covers of flat contramodules

0565896 - MÚ 2023 RIV US eng J - Journal Article
Bazzoni, S. - Positselski, Leonid - Šťovíček, J.
Projective covers of flat contramodules.
International Mathematics Research Notices. Roč. 2022, č. 24 (2022), s. 19527-19564. ISSN 1073-7928. E-ISSN 1687-0247
Institutional support: RVO:67985840
Keywords : Enochs conjecture on covers and direct limits * local splitness * flat contramodules
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1093/imrn/rnab202

We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for infinity-strictly flat contramodules of projective dimension not exceeding 1, using an argument based on the notion of the topological Jacobson radical. Covers and precovers of direct limits of more general classes of objects, both in abelian categories with exact and with nonexact direct limits, are also discussed, with an eye towards the Enochs conjecture about covers and direct limits, using locally split (mono)morphisms as the main technique. In particular, we offer a simple elementary proof of the Enochs conjecture for the left class of an n-tilting cotorsion pair in an abelian category with exact direct limits.
Permanent Link: https://hdl.handle.net/11104/0337372