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@article{2310137,
author = {Almeida, J. and Klíma, Ondřej},
article_number = {1},
doi = {http://dx.doi.org/10.5565/PUBLMAT6712303},
keywords = {profinite algebra; pseudovariety; locally countable; Mal?cev product; factorization forest; Prouhet-Thue-Morse substitution},
language = {eng},
issn = {0214-1493},
journal = {Publicacions Matemátiques},
title = {LOCALLY COUNTABLE PSEUDOVARIETIES},
url = {https://projecteuclid.org/journals/publicacions-matematiques/volume-67/issue-1/LOCALLY-COUNTABLE-PSEUDOVARIETIES/10.5565/PUBLMAT6712303.full},
volume = {67},
year = {2023}
}
TY - JOUR
ID - 2310137
AU - Almeida, J. - Klíma, Ondřej
PY - 2023
TI - LOCALLY COUNTABLE PSEUDOVARIETIES
JF - Publicacions Matemátiques
VL - 67
IS - 1
SP - 127-172
EP - 127-172
PB - Universitat Autonoma de Barcelona
SN - 02141493
KW - profinite algebra
KW - pseudovariety
KW - locally countable
KW - Mal?cev product
KW - factorization forest
KW - Prouhet-Thue-Morse substitution
UR - https://projecteuclid.org/journals/publicacions-matematiques/volume-67/issue-1/LOCALLY-COUNTABLE-PSEUDOVARIETIES/10.5565/PUBLMAT6712303.full
N2 - 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.
ER -
ALMEIDA, J. a Ondřej KLÍMA. LOCALLY COUNTABLE PSEUDOVARIETIES. \textit{Publicacions Matemátiques}. Universitat Autonoma de Barcelona, 2023, roč.~67, č.~1, s.~127-172. ISSN~0214-1493. Dostupné z: https://dx.doi.org/10.5565/PUBLMAT6712303.
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