Document type
Journal articles
Document subtype
Full paper
Title
On formations of monoids
Participants in the publication
Mário J.J. Branco (Author)
Dep. Matemática
CEMAT
Gracinda M. S. Gomes (Author)
Dep. Matemática
CEMAT
Jean-Éric Pin (Author)
Xaro Soler-Escrivà (Author)
Summary
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.
Date of Submisson/Request
2019-11-11
Date of Acceptance
2020-03-27
Date of Publication
2020-04
Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
Where published
Journal of Pure and Applied Algebra
Publication Identifiers
ISSN - 0022-4049
Publisher
Elsevier BV
Document Identifiers
DOI -
https://doi.org/10.1016/j.jpaa.2020.106401
URL -
http://dx.doi.org/10.1016/j.jpaa.2020.106401
Rankings
SCIMAGO Q1 (2020) - 1.075 - Algebra and Number Theory
Keywords
Monoid formation
Group formation
Semigroup