On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup
Cho, Yung Won, Nik Ruškuc · arXiv (Cornell University) · 2024
The monogenic free inverse semigroup $FI_1$ 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 $FI_1$ is finitely presented if and only if it contains only finitely many idempotents. As a consequence, we derive that an inverse subsemigroup of $FI_1$ is finitely presented as a semigroup if and only if it is a finite semilattice.