The Dual Baer Criterion for non-perfect rings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420933" target="_blank" >RIV/00216208:11320/20:10420933 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qWoCH4Phw3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=qWoCH4Phw3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/forum-2019-0028" target="_blank" >10.1515/forum-2019-0028</a>
Alternative languages
Result language
angličtina
Original language name
The Dual Baer Criterion for non-perfect rings
Original language description
Baer's Criterion for Injectivity is a useful tool of the theory of modules. Its dual version (DBC) is known to hold for all right perfect rings, but its validity for the non-right perfect ones is a complex problem (first formulated by C. Faith [Algebra. II. Ring Theory, Springer, Berlin, 1976]). Recently, it has turned out that there are two classes of non-right perfect rings: (1) those for which DBC fails in ZFC, and (2) those for which DBC is independent of ZFC. First examples of rings in the latter class were constructed in [J. Trlifaj, Faith's problem on R-projectivity is undecidable, Proc. Amer. Math. Soc.147 (2019), no. 2, 497-504]; here, we show that this class contains all small semiartinian von Neumann regular rings with primitive factors artinian.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Forum Mathematicum
ISSN
0933-7741
e-ISSN
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Volume of the periodical
2020
Issue of the periodical within the volume
32
Country of publishing house
DE - GERMANY
Number of pages
10
Pages from-to
663-672
UT code for WoS article
000531052300008
EID of the result in the Scopus database
2-s2.0-85078083166