Representations of relatively free profinite semigroups, irreducibility, and order primitivity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114486" target="_blank" >RIV/00216224:14310/20:00114486 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1090/tran/7951" target="_blank" >https://doi.org/10.1090/tran/7951</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/7951" target="_blank" >10.1090/tran/7951</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Representations of relatively free profinite semigroups, irreducibility, and order primitivity

Popis výsledku v původním jazyce

We establish that, under certain closure assumptions on a pseudovariety of semigroups, the corresponding relatively free profinite semigroups freely generated by a nonsingleton finite set act faithfully on their minimum ideals. As applications, we enlarge the scope of several previous join irreducibility results for pseudovarieties of semigroups, which turn out to be even join irreducible in the lattice of pseudovarieties of ordered semigroups, so that, in particular, they are not generated by proper subpseudovarieties of ordered semigroups. We also prove the stronger form of join irreducibility for the Krohn-Rhodes complexity pseudovarieties, thereby solving a problem proposed by Rhodes and Steinberg.

Název v anglickém jazyce

Representations of relatively free profinite semigroups, irreducibility, and order primitivity

Popis výsledku anglicky

We establish that, under certain closure assumptions on a pseudovariety of semigroups, the corresponding relatively free profinite semigroups freely generated by a nonsingleton finite set act faithfully on their minimum ideals. As applications, we enlarge the scope of several previous join irreducibility results for pseudovarieties of semigroups, which turn out to be even join irreducible in the lattice of pseudovarieties of ordered semigroups, so that, in particular, they are not generated by proper subpseudovarieties of ordered semigroups. We also prove the stronger form of join irreducibility for the Krohn-Rhodes complexity pseudovarieties, thereby solving a problem proposed by Rhodes and Steinberg.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA15-02862S" target="_blank" >GA15-02862S: Aplikace algebry a kombinatoriky v teorii formálních jazyků</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Transactions of the American Mathematical Society

ISSN

0002-9947

e-ISSN

1088-6850

Svazek periodika

373

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

41

Strana od-do

1941-1981

Kód UT WoS článku

000516757400016

EID výsledku v databázi Scopus

2-s2.0-85080855269