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.
| Original language | American English |
|---|---|
| Pages (from-to) | 15–25 |
| Journal | Archiv der Mathematik |
| Volume | 120 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2023 |
Bibliographical note
Publisher Copyright:© 2022, Springer Nature Switzerland AG.
Funding
The author is indebted to the reviewer for a number of important suggestions. He is also grateful to Sergey Gusev, Marcel Jackson, and Boris Vernikov for many fruitful discussions on monoid varieties.
ASJC Scopus Subject Areas
- General Mathematics
Keywords
- Lattice of varieties
- Monoid
- Semigroup
- Variety
Disciplines
- Mathematics
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