On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup
Abstract
The monogenic free inverse semigroup FI1 is not finitely presented as a semigroup due to the classic result by Schein (1975). We extend this result and prove that a finitely generated subsemigroup of FI1 is finitely presented if and only if it contains only finitely many idempotents. As a consequence, we derive that an inverse subsemigroup of FI1 is finitely presented as a semigroup if and only if it is a finite semilattice.
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