About the power pseudovariety PCS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00124463" target="_blank" >RIV/00216224:14310/21:00124463 - isvavai.cz</a>
Result on the web
<a href="https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-51/issue-6/About-the-power-pseudovariety-PCS/10.1216/rmj.2021.51.2045.short" target="_blank" >https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-51/issue-6/About-the-power-pseudovariety-PCS/10.1216/rmj.2021.51.2045.short</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1216/rmj.2021.51.2045" target="_blank" >10.1216/rmj.2021.51.2045</a>
Alternative languages
Result language
angličtina
Original language name
About the power pseudovariety PCS
Original language description
The power pseudovariety PCS, that is, the pseudovariety of finite semigroups generated by all power semigroups of finite completely simple semigroups has recently been characterized as the pseudovariety AgBG of all so-called aggregates of block groups. This characterization can be expressed as the equality of pseudovarieties PCS=AgBG. In fact, a longer sequence of equalities of pseudovarieties, namely the sequence of equalities PCS=J∗CS=JⓜCS=AgBG has been verified at the same time. Here, J is the pseudovariety of all ????-trivial semigroups, CS is the pseudovariety of all completely simple semigroups, J∗CS is the pseudovariety generated by the family of all semidirect products of ????-trivial semigroups by completely simple semigroups, and JⓜCS is the pseudovariety generated by the Mal’cev product of the pseudovarieties J and CS. In this paper, another different proof of these equalities is provided first. More precisely, the equalities PCS=J∗CS=JⓜCS are given a new proof, while the equality JⓜCS=AgBG is quoted from a foregoing paper. Subsequently in this paper, this new proof of the mentioned equalities is further refined to yield a proof of the following more general result: For any pseudovariety H of groups, let CS(H) stand for the pseudovariety of all completely simple semigroups whose subgroups belong to H. Then it turns out that, for every locally extensible pseudovariety H of groups, the equalities of pseudovarieties P(CS(H))=J∗CS(H)=JⓜCS(H) hold.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Rocky Mountain Journal of Mathematics
ISSN
0035-7596
e-ISSN
1945-3795
Volume of the periodical
51
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
58
Pages from-to
2045-2102
UT code for WoS article
000772456800012
EID of the result in the Scopus database
2-s2.0-85128124278