On singleton kernel classes in the lattice of varieties of completely regular semigroups
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On singleton kernel classes in the lattice of varieties of completely regular semigroups
Original language description
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).
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-12790S" target="_blank" >GA19-12790S: Effective characterizations of classes of finite semigroups and formal languages</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Algebra and Computation
ISSN
0218-1967
e-ISSN
1793-6500
Volume of the periodical
29
Issue of the periodical within the volume
8
Country of publishing house
SG - SINGAPORE
Number of pages
25
Pages from-to
1383-1407
UT code for WoS article
000492829000002
EID of the result in the Scopus database
2-s2.0-85069861557