Work

On finite presentability of subsemigroups of the monogenic free inverse semigroup

Year: 2024

Type: article

Abstract: 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.

Source: Glasgow Mathematical Journal

DOI: 10.1017/s0017089524000314

Authors: Jung Won Cho, Nik Ruškuc

Institution: University of St Andrews

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: Engineering and Physical Sciences Research Council