About the power pseudovariety PCS
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
About the power pseudovariety PCS
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
About the power pseudovariety PCS
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2021
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Rocky Mountain Journal of Mathematics
ISSN
0035-7596
e-ISSN
1945-3795
Svazek periodika
51
Číslo periodika v rámci svazku
6
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
58
Strana od-do
2045-2102
Kód UT WoS článku
000772456800012
EID výsledku v databázi Scopus
2-s2.0-85128124278