LOCALLY COUNTABLE PSEUDOVARIETIES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134222" target="_blank" >RIV/00216224:14310/23:00134222 - isvavai.cz</a>
Result on the web
<a href="https://projecteuclid.org/journals/publicacions-matematiques/volume-67/issue-1/LOCALLY-COUNTABLE-PSEUDOVARIETIES/10.5565/PUBLMAT6712303.full" target="_blank" >https://projecteuclid.org/journals/publicacions-matematiques/volume-67/issue-1/LOCALLY-COUNTABLE-PSEUDOVARIETIES/10.5565/PUBLMAT6712303.full</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5565/PUBLMAT6712303" target="_blank" >10.5565/PUBLMAT6712303</a>
Alternative languages
Result language
angličtina
Original language name
LOCALLY COUNTABLE PSEUDOVARIETIES
Original language description
The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are countable, which are said to be locally countable. We also call locally countable a pseudovariety V (of finite semigroups) for which all pro -V semigroups are locally countable. We investigate operations preserving local countability of pseudovarieties and show that, in contrast with local finiteness, sev-eral natural operations do not preserve it. We also investigate the relationship of a finitely generated profinite semigroup being countable with every element being ex-pressible in terms of the generators using multiplication and the idempotent (omega) power. The two properties turn out to be equivalent if there are only countably many group elements, gathered in finitely many regular J-classes. We also show that the pseudovariety generated by all finite ordered monoids satisfying the inequality 1 5 xn is locally countable if and only if n = 1.
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Publicacions Matemátiques
ISSN
0214-1493
e-ISSN
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Volume of the periodical
67
Issue of the periodical within the volume
1
Country of publishing house
ES - SPAIN
Number of pages
46
Pages from-to
127-172
UT code for WoS article
000964068600003
EID of the result in the Scopus database
2-s2.0-85148034209