Covers and direct limits: A contramodule-based approach

0545496 - MÚ 2022 RIV DE eng J - Článek v odborném periodiku
Bazzoni, S. - Positselski, Leonid
Covers and direct limits: A contramodule-based approach.
Mathematische Zeitschrift. Roč. 299, 1-2 (2021), s. 1-52. ISSN 0025-5874. E-ISSN 1432-1823
Grant CEP: GA ČR(CZ) GA20-13778S
Institucionální podpora: RVO:67985840
Klíčová slova: Enochs conjecture * generalized tilting theory * topologically perfect topological rings
Obor OECD: Pure mathematics
Impakt faktor: 0.820, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s00209-020-02654-x

We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits. In the n-tilting–cotilting correspondence context, if A is a Grothendieck abelian category and the related abelian category B is equivalent to the category of contramodules over a topological ring R belonging to one of certain four classes of topological rings (e. g., R is commutative), then the left tilting class is covering in A if and only if it is closed under direct limits in A, and if and only if all the discrete quotient rings of the topological ring R are perfect. Generally, if M is a module satisfying a certain telescope Hom exactness condition (e. g., M is Σ-pure-Ext^1-self-orthogonal) and the topological ring R of endomorphisms of M belongs to one of some seven classes of topological rings, then the class Add(M) is closed under direct limits if and only if every countable direct limit of copies of M has an Add(M)-cover, and if and only if M has perfect decomposition.
Trvalý link: http://hdl.handle.net/11104/0322177