Inherently Non-Finitely Generated Varieties of Aperiodic Monoids with Central Idempotents
Journal of Mathematical Sciences
Monoid, Aperiodic monoid, Central idempotent, Variety, Finitely generated, Inherently non-finitely generated
Let A denote the class of aperiodic monoids with central idempotents. A subvariety of A that is not contained in any finitely generated subvariety of A is said to be inherently non-finitely generated. A characterization of inherently non-finitely generated subvarieties of A, based on identities that they cannot satisfy and monoids that they must contain, is given. It turns out that there exists a unique minimal inherently non-finitely generated subvariety of A, the inclusion of which is both necessary and sufficient for a subvariety of A to be inherently non-finitely generated. Further, it is decidable in polynomial time if a finite set of identities defines an inherently non-finitely generated subvariety of A.
Lee, Edmond W. H., "Inherently Non-Finitely Generated Varieties of Aperiodic Monoids with Central Idempotents" (2015). Mathematics Faculty Articles. 13.