Contramodules over pro-perfect topological rings

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00551157" target="_blank" >RIV/67985840:_____/22:00551157 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1515/forum-2021-0010" target="_blank" >https://doi.org/10.1515/forum-2021-0010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/forum-2021-0010" target="_blank" >10.1515/forum-2021-0010</a>

Result language

angličtina

Original language name

Contramodules over pro-perfect topological rings

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Forum Mathematicum

ISSN

0933-7741

e-ISSN

1435-5337

Volume of the periodical

34

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

39

Pages from-to

1-39

UT code for WoS article

000737425500001

EID of the result in the Scopus database

2-s2.0-85120616208