Regular semigroups weakly generated by one element

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

Autores

Luís Oliveira (Autor) FCUP

Revista

Título: Semigroup Forum

Vol. 107

Páginas: 525-563

ISSN: 0037-1912

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00Z-5VW

DOI: 10.1007/s00233-023-10389-4

Abstract (EN): In this paper we study the regular semigroups weakly generated by a single element x, that is, with no proper regular subsemigroup containing x. We show there exists a regular semigroup F-1 weakly generated by x such that all other regular semigroups weakly generated by x are homomorphic images of F-1. We define F-1 using a presentation where both sets of generators and relations are infinite. Nevertheless, the word problem for this presentation is decidable. We describe a canonical form for the congruence classes given by this presentation, and explain how to obtain it. We end the paper studying the structure of F-1. In particular, we show that the 'free regular semigroup FI2 weakly generated by two idempotents' is isomorphic to a regular subsemigroup of F-1 weakly generated by {xx', x' x}.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 39