Varieties Generated by 2-testable Monoids

Authors

Edmond W. H. Lee, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

12-1-2012

Publication Title

Studia Scientiarum Mathematicarum Hungarica

Keywords

Primary 20M07, Monoid, Semigroup, Finitely based, Variety, Non-finitely based

ISSN

0081-6906

Volume

49

Issue/No.

3

First Page

366

Last Page

389

Abstract

The smallest monoid containing a 2-testable semigroup is defined to be a 2-testable monoid. The well-known Brandt monoid B₂¹ of order six is an example of a 2-testable monoid. The finite basis problem for 2-testable monoids was recently addressed and solved. The present article continues with the investigation by describing all monoid varieties generated by 2-testable monoids. It is shown that there are 28 such varieties, all of which are finitely generated and precisely 19 of which are finitely based. As a comparison, the subvariety lattice of the monoid variety generated by the monoid B₂¹ is examined. This lattice has infinite width, satisfies neither the ascending chain condition nor the descending chain condition, and contains non-finitely generated varieties.

NSUWorks Citation

Lee, Edmond W. H., "Varieties Generated by 2-testable Monoids" (2012). Mathematics Faculty Articles. 7.
https://nsuworks.nova.edu/math_facarticles/7

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1556/SScMath.49.2012.3.1211