Mathematics Faculty Articles

Title

Varieties Generated by 2-testable Monoids

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.

ORCID ID

0000-0002-1662-3734

ResearcherID

I-6970-2013

DOI

10.1556/SScMath.49.2012.3.1211

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