On formations of monoids
| Autor: | Mário J. J. Branco, Jean-Eric Pin, Xaro Soler-Escrivà, Gracinda M. S. Gomes |
|---|---|
| Přispěvatelé: | Universidad de Alicante. Departamento de Matemáticas, Grupo de Álgebra y Geometría (GAG), CEMAT-Ciências and Dep. Matemática da Faculdade de Ciências da Universidade de Lisboa, Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Dpt. de Matemàtiques, Universitat d’Alacant |
| Rok vydání: | 2020 |
| Předmět: |
Monoid
Class (set theory) Pure mathematics Algebra and Number Theory Group formation Semigroup 010102 general mathematics Monoid formation Minimal ideal Lattice (discrete subgroup) 01 natural sciences Álgebra Mathematics::Category Theory 0103 physical sciences 010307 mathematical physics Isomorphism 0101 mathematics Algebraic number Connection (algebraic framework) [MATH]Mathematics [math] ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | RUA. Repositorio Institucional de la Universidad de Alicante Universidad de Alicante (UA) Journal of Pure and Applied Algebra Journal of Pure and Applied Algebra, Elsevier, 2020, 224 (11), pp.106401. ⟨10.1016/j.jpaa.2020.106401⟩ |
| ISSN: | 0022-4049 |
| Popis: | 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. 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). |
| Databáze: | OpenAIRE |
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