Tipo
Artigos em Revista
Tipo de Documento
Artigo Completo
Título
On formations of monoids
Participantes na publicação
Mário J.J. Branco (Author)
Dep. Matemática
CEMAT
Gracinda M. S. Gomes (Author)
Dep. Matemática
CEMAT
Jean-Éric Pin (Author)
Xaro Soler-Escrivà (Author)
Resumo
A formation of monoids is a class of finite monoids closed under taking quotients and subdirect products. Formations of monoids were first studied in connection with formal language theory, but in this paper, we come back to an algebraic point of view. We give two natural constructions of formations based on constraints on the minimal ideal and on the maximal subgroups of a monoid. Next we describe two sublattices of the lattice of all formations, and give, for each of them, an isomorphism with a known lattice of varieties of monoids. Finally, we study formations and varieties containing only Clifford monoids, completely describe such varieties and discuss the case of formations.
Data de Submissão/Pedido
2019-11-11
Data de Aceitação
2020-03-27
Data de Publicação
2020-04
Instituição
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
Suporte
Journal of Pure and Applied Algebra
Identificadores da Publicação
ISSN - 0022-4049
Editora
Elsevier BV
Identificadores do Documento
DOI -
https://doi.org/10.1016/j.jpaa.2020.106401
URL -
http://dx.doi.org/10.1016/j.jpaa.2020.106401
Identificadores de Qualidade
SCIMAGO Q1 (2020) - 1.075 - Algebra and Number Theory
Keywords
Monoid formation
Group formation
Semigroup