On formations of monoids

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Title: On formations of monoids
Authors: Branco, Mário J.J. | Gomes, Gracinda M.S. | Pin, Jean-Éric | Soler-Escrivà, Xaro
Research Group/s: Grupo de Álgebra y Geometría (GAG)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Monoid formation | Group formation | Semigroup
Knowledge Area: Álgebra
Issue Date: Nov-2020
Publisher: Elsevier
Citation: Journal of Pure and Applied Algebra. 2020, 224(11): 106401. doi:10.1016/j.jpaa.2020.106401
Abstract: 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.
Sponsor: The first and second authors received financial support from Fundação para a Ciência e a Tecnologia (FCT) through the following four projects: UID/MULTI/04621/2013, UIDB/04621/2020 and UIDP/04621/2020 of CEMAT at Faculdade de Ciências, Universidade de Lisboa, and project PTDC/MAT-PUR/31174/2017. The third author is partially funded by the DeLTA project (ANR-16-CE40-0007).
URI: http://hdl.handle.net/10045/107433
ISSN: 0022-4049 (Print) | 1873-1376 (Online)
DOI: 10.1016/j.jpaa.2020.106401
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2020 Elsevier B.V.
Peer Review: si
Publisher version: https://doi.org/10.1016/j.jpaa.2020.106401
Appears in Collections:INV - GAG - Artículos de Revistas

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