Cross varieties of aperiodic monoids with central idempotents
Edmond W. H. Lee · Portugaliae Mathematica · 2011
Let \boldsymbol A denote the class of all aperiodic monoids with central idempotents. A description of all Cross subvarieties of \boldsymbol A , based on identities that they satisfy and monoids that they cannot contain, is given. The two limit subvarieties of \boldsymbol A , published by Marcel Jackson in 2005, turn out to be the only finitely generated, almost Cross subvarieties of \boldsymbol A . It follows that it is decidable in quartic time if a finite monoid in \boldsymbol A generates a Cross variety.