Key points are not available for this paper at this time.
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.
Cho et al. (Mon,) studied this question.