Authors: E W H Lee
Publish Date: 2015/08/05
Volume: 209, Issue: 4, Pages: 588-599
Abstract
Let Open image in new window denote the class of aperiodic monoids with central idempotents A subvariety of Open image in new window that is not contained in any finitely generated subvariety of Open image in new window is said to be inherently nonfinitely generated A characterization of inherently nonfinitely generated subvarieties of Open image in new window 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 nonfinitely generated subvariety of Open image in new window the inclusion of which is both necessary and sufficient for a subvariety of Open image in new window to be inherently nonfinitely generated Further it is decidable in polynomial time if a finite set of identities defines an inherently nonfinitely generated subvariety of Open image in new window
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