Let 
denote the class of aperiodic monoids with central idempotents. A subvariety of 
that is not contained in any finitely generated subvariety of 
is said to be inherently non-finitely generated. A characterization of inherently non-finitely generated subvarieties of 
, 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 
, the inclusion of which is both necessary and sufficient for a subvariety of 
to be inherently non-finitely generated. Further, it is decidable in polynomial time if a finite set of identities defines an inherently nonfinitely generated subvariety of 
.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, pp. 166–182.
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Lee, E.W.H. Inherently Non-Finitely Generated Varieties of Aperiodic Monoids with Central Idempotents. J Math Sci 209, 588–599 (2015). https://doi.org/10.1007/s10958-015-2515-1
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DOI: https://doi.org/10.1007/s10958-015-2515-1