Covering classes and uniserial modules

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436493" target="_blank" >RIV/00216208:11320/21:10436493 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=V~dLXZXjJK" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=V~dLXZXjJK</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2020.11.011" target="_blank" >10.1016/j.jalgebra.2020.11.011</a>

Result language
angličtina
Original language name
Covering classes and uniserial modules
Original language description
We apply minimal weakly generating sets to study the existence of Add(U-R)-covers for a uniserial module U-R. If U-R is a uniserial right module over a ring R, then S := End(U-R) has at most two maximal (right, left, two-sided) ideals: one is the set I of all endomorphisms that are not injective, and the other is the set K of all endomorphisms of U-R that are not surjective. We prove that if U-R is either finitely generated, or artinian, or I subset of K, then the class Add(U-R) is covering if and only if it is closed under direct limit. Moreover, we study endomorphism rings of artinian uniserial modules giving several examples. (C) 2020 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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/GA17-23112S" target="_blank" >GA17-23112S: Structure theory for representations of algebras (localization and tilting theory)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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