Small Semigroups Generating Varieties with Continuum Many Subvarieties

Authors

Charles C. Edmunds, Mount Saint Vincent University
Edmond W. H. Lee, Simon Fraser UniversityFollow
Ken W.K. Lee, City University of Hong Kong

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.

Comments

Mathematics Subject Classifications (2000)

20M07

08B15

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