LOCALLY COUNTABLE PSEUDOVARIETIES

• Tipo: Artigo em Revista Científica Internacional
• Data: 2023

Autores

Almeida, J (Autor) FCUP; Klfma, O (Autor) Outra

Revista

Título: Publicacions Matematiques

Vol. 67

Páginas: 127-172

ISSN: 0214-1493

Editora: Universitat de Barcelona

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00X-R1D

DOI: 10.5565/publmat6712303

Abstract (EN): 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 46