On a locality-like property of the pseudovariety J

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00106425" target="_blank" >RIV/00216224:14310/18:00106425 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs10998-017-0186-z.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10998-017-0186-z" target="_blank" >10.1007/s10998-017-0186-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On a locality-like property of the pseudovariety J

Popis výsledku v původním jazyce

It is well known that the pseudovariety J of all J-trivial monoids is not local, which means that the pseudovariety gJ of categories generated by J is a proper subpseudovariety of the pseudovariety lJ of categories all of whose local monoids belong to J. In this paper, it is proved that the pseudovariety J enjoys the following weaker property. For every prime number p, the pseudovariety lJ is a subpseudovariety of the pseudovariety g(J*Abp), where Abp is the pseudovariety of all elementary abelian p-groups and J*Abp is the pseudovariety of monoids generated by the class of all semidirect products of monoids from J by groups from Abp. As an application, a new proof of the celebrated equality of pseudovarieties PG=BG is obtained, where PG is the pseudovariety of monoids generated by the class of all power monoids of groups and BG is the pseudovariety of all block groups.

Název v anglickém jazyce

On a locality-like property of the pseudovariety J

Popis výsledku anglicky

It is well known that the pseudovariety J of all J-trivial monoids is not local, which means that the pseudovariety gJ of categories generated by J is a proper subpseudovariety of the pseudovariety lJ of categories all of whose local monoids belong to J. In this paper, it is proved that the pseudovariety J enjoys the following weaker property. For every prime number p, the pseudovariety lJ is a subpseudovariety of the pseudovariety g(J*Abp), where Abp is the pseudovariety of all elementary abelian p-groups and J*Abp is the pseudovariety of monoids generated by the class of all semidirect products of monoids from J by groups from Abp. As an application, a new proof of the celebrated equality of pseudovarieties PG=BG is obtained, where PG is the pseudovariety of monoids generated by the class of all power monoids of groups and BG is the pseudovariety of all block groups.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Periodica mathematica Hungarica

ISSN

0031-5303

e-ISSN

1588-2829

Svazek periodika

76

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

46

Strana od-do

1-46

Kód UT WoS článku

000425544200001

EID výsledku v databázi Scopus

2-s2.0-85019757437