Profinite Congruences and Unary Algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139497" target="_blank" >RIV/00216224:14310/24:00139497 - isvavai.cz</a>
Result on the web
<a href="https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-42-number-4-2024/mvlsc-42-4-p-265-297/" target="_blank" >https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-42-number-4-2024/mvlsc-42-4-p-265-297/</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Profinite Congruences and Unary Algebras
Original language description
Profinite congruences on profinite algebras determining profinite quotients are difficult to describe. In particular, no constructive description is known of the least profinite congruence containing a given binary relation on the algebra. On the other hand, closed congruences and fully invariant congruences can be described constructively. In a previous paper, we conjectured that fully invariant closed congruences on a relatively free profinite algebra are always profinite. Here, we show that our conjecture fails for unary algebras and that closed congruences on relatively free profinite semigroups are not necessarily profinite. As part of our study of unary algebras, we establish an adjunction between profinite unary algebras and profinite monoids. We also show that the Polish representation of the free profinite unary algebra is faithful.
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/GA19-12790S" target="_blank" >GA19-12790S: Effective characterizations of classes of finite semigroups and formal languages</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Multiple-Valued Logic and Soft Computing
ISSN
1542-3980
e-ISSN
1542-3999
Volume of the periodical
42
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
265-297
UT code for WoS article
001269856600002
EID of the result in the Scopus database
2-s2.0-85200538964