Mathematics Faculty Articles

Title

A minimal pseudo-complex monoid

Document Type

Article

Publication Date

11-27-2022

Publication Title

Archiv der Mathematik

Keywords

Monoid, Semigroup, Variety, Lattice of varieties

ISSN

0003-889X

Abstract

A monoid is pseudo-complex if the semigroup variety it generates has uncountably many subvarieties, while the monoid variety it generates has only finitely many subvarieties. The smallest pseudo-complex monoid currently known is of order seven. The present article exhibits a pseudo-complex monoid of order six and shows that every smaller monoid is not pseudo-complex. Consequently, minimal pseudo-complex monoids are of order six.

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1007/s00013-022-01797-z

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