On singleton kernel classes in the lattice of varieties of
completely regular semigroups

J 2019

On singleton kernel classes in the lattice of varieties of completely regular semigroups

KAĎOUREK, Jiří

Základní údaje

Originální název

On singleton kernel classes in the lattice of varieties of completely regular semigroups

Autoři

KAĎOUREK, Jiří

Vydání

International Journal of Algebra and Computation, Singapore, World Scientific, 2019, 0218-1967

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Singapur

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.512

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/19:00108180

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Completely regular semigroups; varieties of completely regular semigroups; kernel and trace classes in the lattice of varieties of completely regular semigroups; relatively free completely regular semigroups.

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 30. 3. 2020 19:47, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper, it is shown that, for every non-trivial variety U of groups, the variety HU of all completely regular semigroups all of whose subgroups belong to U is minimal in its kernel class in the lattice L(CR) of all varieties of completely regular semigroups, and hence it constitutes, in fact, a singleton kernel class in the lattice L(CR). Even more generally, it is shown that, for every variety V of completely simple semigroups which does not consist entirely of rectangular groups, the variety DV of all completely regular semigroups all of whose completely simple subsemigroups belong to V is minimal in its kernel class in the lattice L(CR), and hence it likewise constitutes a singleton kernel class in the mentioned lattice L(CR).

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 singleton kernel classes in the lattice of varieties of completely regular semigroups. International Journal of Algebra and Computation. Singapore: World Scientific, 2019, roč. 29, č. 8, s. 1383-1407. ISSN 0218-1967. Dostupné z: https://doi.org/10.1142/S0218196719500541.

@article{1634742,
   author = {Kaďourek, Jiří},
   article_location = {Singapore},
   article_number = {8},
   doi = {https://doi.org/10.1142/S0218196719500541},
   keywords = {Completely regular semigroups; varieties of completely regular semigroups; kernel and trace classes in the lattice of varieties of completely regular semigroups; relatively free completely regular semigroups.},
   language = {eng},
   issn = {0218-1967},
   journal = {International Journal of Algebra and Computation},
   title = {On singleton kernel classes in the lattice of varieties of completely regular semigroups},
   url = {https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541},
   volume = {29},
   year = {2019}
}

TY  - JOUR
ID  - 1634742
AU  - Kaďourek, Jiří
PY  - 2019
TI  - On singleton kernel classes in the lattice of varieties of completely regular semigroups
JF  - International Journal of Algebra and Computation
VL  - 29
IS  - 8
SP  - 1383-1407
EP  - 1383-1407
PB  - World Scientific
SN  - 02181967
KW  - Completely regular semigroups
KW  - varieties of completely regular semigroups
KW  - kernel and trace classes in the lattice of varieties of completely regular semigroups
KW  - relatively free completely regular semigroups.
UR  - https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541
L2  - https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541
N2  - In this paper, it is shown that, for every non-trivial variety U of groups, the variety HU of all completely regular semigroups all of whose subgroups belong to U is minimal in its kernel class in the lattice L(CR) of all varieties of completely regular semigroups, and hence it constitutes, in fact, a singleton kernel class in the lattice L(CR). Even more generally, it is shown that, for every variety V of completely simple semigroups which does not consist entirely of rectangular groups, the variety DV of all completely regular semigroups all of whose completely simple subsemigroups belong to V is minimal in its kernel class in the lattice L(CR), and hence it likewise constitutes a singleton kernel class in the mentioned lattice L(CR).
ER  -

KAĎOUREK, Jiří. On singleton kernel classes in the lattice of varieties of completely regular semigroups. \textit{International Journal of Algebra and Computation}. Singapore: World Scientific, 2019, roč.~29, č.~8, s.~1383-1407. ISSN~0218-1967. Dostupné z: https://doi.org/10.1142/S0218196719500541.

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