Abstract
A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been available since the early 1970s, but it is unknown if there exists a finitely universal variety of monoids. The main objective of the present article is to exhibit the first examples of finitely universal varieties of monoids. The finite universality of these varieties is established by showing that the lattice of equivalence relations on every sufficiently large finite set is anti-isomorphic to some subinterval of the lattice of subvarieties.
| Original language | American English |
|---|---|
| Pages (from-to) | 762–775 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 52 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 31 2020 |
Bibliographical note
Publisher Copyright:© 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
Funding
The first author was supported by the Ministry of Science and Higher Education of the Russian Federation (project FEUZ‐2020‐0016).
| Funders | Funder number |
|---|---|
| Ministry of Education and Science of the Russian Federation | FEUZ‐2020‐0016 |
| Ministry of Education and Science of the Russian Federation |
ASJC Scopus Subject Areas
- General Mathematics
Disciplines
- Mathematics
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