Mathematics Faculty Articles

Document Type

Article

Publication Date

1-7-2021

Publication Title

arXiv Preprint

Keywords

Monoid, Variety, Lattice of varieties, Cancellable element of a lattice, Modular element of a lattice

Abstract

The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements.

Comments

The first author is supported by the Ministry of Science and Higher Education of the Russian Federation (project FEUZ-2020-0016).

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

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Mathematics Commons

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