Mathematics Faculty Articles
Small Semigroups Generating Varieties with Continuum Many Subvarieties
Document Type
Article
Publication Date
3-2010
Publication Title
Order
Keywords
Semigroups, Monoids, Varieties, Finitely based, Hereditarily finitely based
ISSN
0167-8094
Volume
27
Issue/No.
1
First Page
83
Last Page
100
Abstract
The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.
NSUWorks Citation
Edmunds, Charles C.; Lee, Edmond W. H.; and Lee, Ken W.K., "Small Semigroups Generating Varieties with Continuum Many Subvarieties" (2010). Mathematics Faculty Articles. 153.
https://nsuworks.nova.edu/math_facarticles/153
ORCID ID
0000-0002-1662-3734
ResearcherID
I-6970-2013
DOI
10.1007/s11083-010-9142-8
Comments
Mathematics Subject Classifications (2000)
20M07
08B15