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Publication details

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-Ciências - Centro de Matemática Computacional e Estocástica-Ciências
Gracinda M. S. Gomes (Author)
Dep. Matemática
CEMAT-Ciências - Centro de Matemática Computacional e Estocástica-Ciências
Jean-Éric Pin (Author)
Xaro Soler-Escrivà (Author)

Scope
International

Refereeing
Yes

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

Number of pages
24

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 (2019) - 1.003 - Algebra and Number Theory

Keywords
Monoid formation Group formation Semigroup


Export

APA
Mário J.J. Branco, Gracinda M. S. Gomes, Jean-Éric Pin, Xaro Soler-Escrivà, (2020). On formations of monoids. Journal of Pure and Applied Algebra, ISSN 0022-4049. eISSN . http://dx.doi.org/10.1016/j.jpaa.2020.106401

IEEE
Mário J.J. Branco, Gracinda M. S. Gomes, Jean-Éric Pin, Xaro Soler-Escrivà, "On formations of monoids" in Journal of Pure and Applied Algebra, 2020. 10.1016/j.jpaa.2020.106401

BIBTEX
@article{44567, author = {Mário J.J. Branco and Gracinda M. S. Gomes and Jean-Éric Pin and Xaro Soler-Escrivà}, title = {On formations of monoids}, journal = {Journal of Pure and Applied Algebra}, year = 2020, }