Contramodules over pro-perfect topological rings

0551157 - MÚ 2023 RIV DE eng J - Journal Article
Positselski, Leonid
Contramodules over pro-perfect topological rings.
Forum Mathematicum. Roč. 34, č. 1 (2022), s. 1-39. ISSN 0933-7741. E-ISSN 1435-5337
R&D Projects: GA ČR(CZ) GA20-13778S
Institutional support: RVO:67985840
Keywords : Enochs conjecture * flat contramodules * projective covers
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
https://doi.org/10.1515/forum-2021-0010

For four wide classes of topological rings R, we show that all flat left R-contramodules have projective covers if and only if all flat left R-contramodules are projective if and only if all left R-contramodules have projective covers if and only if all descending chains of cyclic discrete right R-modules terminate if and only if all the discrete quotient rings of R are left perfect. Three classes of topological rings for which this holds are the complete, separated topological associative rings with a base of neighborhoods of zero formed by open two-sided ideals such that either the ring is commutative, or it has a countable base of neighborhoods of zero, or it has only a finite number of semisimple discrete quotient rings. The fourth class consists of some topological rings with a base of open right ideals, it is a generalization of the first three classes. The key technique on which the proofs are based is the contramodule Nakayama lemma for topologically T-nilpotent ideals.
Permanent Link: http://hdl.handle.net/11104/0326605