Varieties of Monoids with Complex Lattices of Subvarieties

Authors

Sergey V. Gusev, Ural Federal University - Ekaterinburg, Russia
Edmond W. H. Lee, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

8-31-2020

Publication Title

Bulletin of the London Mathematical Society

ISSN

0024-6093

Volume

52

Issue/No.

4

First Page

762

Last Page

755

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.

NSUWorks Citation

Gusev, Sergey V. and Lee, Edmond W. H., "Varieties of Monoids with Complex Lattices of Subvarieties" (2020). Mathematics Faculty Articles. 292.
https://nsuworks.nova.edu/math_facarticles/292

DOI

10.1112/blms.12392