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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00108180" target="_blank" >RIV/00216224:14310/19:00108180 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/S0218196719500541</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218196719500541" target="_blank" >10.1142/S0218196719500541</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

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

Popis výsledku anglicky

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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-12790S" target="_blank" >GA19-12790S: Efektivní charakterizace tříd konečných pologrup a formálních jazyků</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Algebra and Computation

ISSN

0218-1967

e-ISSN

1793-6500

Svazek periodika

29

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

25

Strana od-do

1383-1407

Kód UT WoS článku

000492829000002

EID výsledku v databázi Scopus

2-s2.0-85069861557