REPRESENTATIONS OF RELATIVELY FREE PROFINITE SEMIGROUPS, IRREDUCIBILITY, AND ORDER PRIMITIVITY

• Tipo: Artigo em Revista Científica Internacional
• Data: 2020

Autores

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

Revista

Título: Transactions of the American Mathematical Society

Vol. 373

Páginas: 1941-1981

ISSN: 0002-9947

Editora: American Mathematical Society

Indexação

ISI Web of Knowledge - 4 Citações

Scopus - 4 Citações

Outras Informações

ID Authenticus: P-00R-VWE

DOI: 10.1090/tran/7951

Abstract (EN): 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 41