Varieties generated by 2-testable monoids

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.