On semidirectly closed pseudovarieties of finite semigroups and
monoids

J 2022

On semidirectly closed pseudovarieties of finite semigroups and monoids

KAĎOUREK, Jiří

Základní údaje

Originální název

On semidirectly closed pseudovarieties of finite semigroups and monoids

Autoři

KAĎOUREK, Jiří

Vydání

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, ENGLAND, CAMBRIDGE UNIV PRESS, 2022, 0008-4395

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.600

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00129145

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

semidirect product of semigroups; semidirectly closed pseudovariety of finite semigroups; local pseudovariety of finite monoids

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 30. 8. 2022 16:05, doc. RNDr. Jiří Kaďourek, CSc.

Anotace

V originále

For every pseudovariety V of finite monoids, let LV denote the pseudovariety of all finite semigroups all of whose local submonoids belong to V. In this paper, it is shown that, for every nontrivial semidirectly closed pseudovariety V of finite monoids, the pseudovariety LV of finite semigroups is also semidirectly closed if, and only if, the given pseudovariety V is local in the sense of Tilson. This finding resolves a long-standing open problem posed in the second volume of the classic monograph by Eilenberg.

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

KAĎOUREK, Jiří. On semidirectly closed pseudovarieties of finite semigroups and monoids. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES. ENGLAND: CAMBRIDGE UNIV PRESS, 2022, roč. 65, č. 3, s. 612-627. ISSN 0008-4395. Dostupné z: https://doi.org/10.4153/S0008439521000564.

@article{2214101,
   author = {Kaďourek, Jiří},
   article_location = {ENGLAND},
   article_number = {3},
   doi = {https://doi.org/10.4153/S0008439521000564},
   keywords = {semidirect product of semigroups; semidirectly closed pseudovariety of finite semigroups; local pseudovariety of finite monoids},
   language = {eng},
   issn = {0008-4395},
   journal = {CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES},
   title = {On semidirectly closed pseudovarieties of finite semigroups and monoids},
   url = {https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C97088F30E561DB1FDD6F5A20DC414D5/S0008439521000564a.pdf/on-semidirectly-closed-pseudovarieties-of-finite-semigroups-and-monoids.pdf},
   volume = {65},
   year = {2022}
}

TY  - JOUR
ID  - 2214101
AU  - Kaďourek, Jiří
PY  - 2022
TI  - On semidirectly closed pseudovarieties of finite semigroups and monoids
JF  - CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
VL  - 65
IS  - 3
SP  - 612-627
EP  - 612-627
PB  - CAMBRIDGE UNIV PRESS
SN  - 00084395
KW  - semidirect product of semigroups
KW  - semidirectly closed pseudovariety of finite semigroups
KW  - local pseudovariety of finite monoids
UR  - https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C97088F30E561DB1FDD6F5A20DC414D5/S0008439521000564a.pdf/on-semidirectly-closed-pseudovarieties-of-finite-semigroups-and-monoids.pdf
N2  - For every pseudovariety V of finite monoids, let LV denote the pseudovariety of all finite semigroups all of whose local submonoids belong to V. In this paper, it is shown that, for every nontrivial semidirectly closed pseudovariety V of finite monoids, the pseudovariety LV of finite semigroups is also semidirectly closed if, and only if, the given pseudovariety V is local in the sense of Tilson. This finding resolves a long-standing open problem posed in the second volume of the classic monograph by Eilenberg.
ER  -

KAĎOUREK, Jiří. On semidirectly closed pseudovarieties of finite semigroups and monoids. \textit{CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES}. ENGLAND: CAMBRIDGE UNIV PRESS, 2022, roč.~65, č.~3, s.~612-627. ISSN~0008-4395. Dostupné z: https://doi.org/10.4153/S0008439521000564.

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