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Contramodules over pro-perfect topological rings
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SYSNO ASEP 0551157 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Contramodules over pro-perfect topological rings Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID Source Title Forum Mathematicum. - : Walter de Gruyter - ISSN 0933-7741
Roč. 34, č. 1 (2022), s. 1-39Number of pages 39 s. Language eng - English Country DE - Germany Keywords Enochs conjecture ; flat contramodules ; projective covers 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 000737425500001 EID SCOPUS 85120616208 DOI 10.1515/forum-2021-0010 Annotation 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. 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/10.1515/forum-2021-0010
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