LOCALLY COUNTABLE PSEUDOVARIETIES

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134222" target="_blank" >RIV/00216224:14310/23:00134222 - isvavai.cz</a>

Výsledek na webu

<a href="https://projecteuclid.org/journals/publicacions-matematiques/volume-67/issue-1/LOCALLY-COUNTABLE-PSEUDOVARIETIES/10.5565/PUBLMAT6712303.full" target="_blank" >https://projecteuclid.org/journals/publicacions-matematiques/volume-67/issue-1/LOCALLY-COUNTABLE-PSEUDOVARIETIES/10.5565/PUBLMAT6712303.full</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5565/PUBLMAT6712303" target="_blank" >10.5565/PUBLMAT6712303</a>

Jazyk výsledku

angličtina

Název v původním jazyce

LOCALLY COUNTABLE PSEUDOVARIETIES

Popis výsledku v původním jazyce

The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are countable, which are said to be locally countable. We also call locally countable a pseudovariety V (of finite semigroups) for which all pro -V semigroups are locally countable. We investigate operations preserving local countability of pseudovarieties and show that, in contrast with local finiteness, sev-eral natural operations do not preserve it. We also investigate the relationship of a finitely generated profinite semigroup being countable with every element being ex-pressible in terms of the generators using multiplication and the idempotent (omega) power. The two properties turn out to be equivalent if there are only countably many group elements, gathered in finitely many regular J-classes. We also show that the pseudovariety generated by all finite ordered monoids satisfying the inequality 1 5 xn is locally countable if and only if n = 1.

Název v anglickém jazyce

LOCALLY COUNTABLE PSEUDOVARIETIES

Popis výsledku anglicky

The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemigroups are countable, which are said to be locally countable. We also call locally countable a pseudovariety V (of finite semigroups) for which all pro -V semigroups are locally countable. We investigate operations preserving local countability of pseudovarieties and show that, in contrast with local finiteness, sev-eral natural operations do not preserve it. We also investigate the relationship of a finitely generated profinite semigroup being countable with every element being ex-pressible in terms of the generators using multiplication and the idempotent (omega) power. The two properties turn out to be equivalent if there are only countably many group elements, gathered in finitely many regular J-classes. We also show that the pseudovariety generated by all finite ordered monoids satisfying the inequality 1 5 xn is locally countable if and only if n = 1.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-12790S" target="_blank" >GA19-12790S: Efektivní charakterizace tříd konečných pologrup a formálních jazyků</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Publicacions Matemátiques

ISSN

0214-1493

e-ISSN

—

Svazek periodika

67

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

46

Strana od-do

127-172

Kód UT WoS článku

000964068600003

EID výsledku v databázi Scopus

2-s2.0-85148034209