LOCALLY COUNTABLE PSEUDOVARIETIES

J 2023

LOCALLY COUNTABLE PSEUDOVARIETIES

ALMEIDA, J. a Ondřej KLÍMA

Základní údaje

Originální název

LOCALLY COUNTABLE PSEUDOVARIETIES

Autoři

ALMEIDA, J. a Ondřej KLÍMA

Vydání

Publicacions Matemátiques, Universitat Autonoma de Barcelona, 2023, 0214-1493

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Španělsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.800

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/23:00134222

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

profinite algebra; pseudovariety; locally countable; Mal?cev product; factorization forest; Prouhet-Thue-Morse substitution

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 12. 9. 2023 13:46, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA19-12790S, projekt VaV

Název: Efektivní charakterizace tříd konečných pologrup a formálních jazyků

Investor: Grantová agentura ČR, Efektivní charakterizace tříd konečných pologrup a formálních jazyků

Citovat

ALMEIDA, J. a Ondřej KLÍMA. LOCALLY COUNTABLE PSEUDOVARIETIES. Publicacions Matemátiques. Universitat Autonoma de Barcelona, 2023, roč. 67, č. 1, s. 127-172. ISSN 0214-1493. Dostupné z: https://doi.org/10.5565/PUBLMAT6712303.

@article{2310137,
   author = {Almeida, J. and Klíma, Ondřej},
   article_number = {1},
   doi = {https://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://doi.org/10.5565/PUBLMAT6712303.

Přehled o publikaci