On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup

2024/04/08 by Y. Cho, Nik Ruškuc, Cho, Yung Won +1
Computer Science · Engineering · #20M05 #20M18 #Control and Dynamics of Mobile Robots #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2404.05244

openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Generators and presentations of inverse subsemigroups of the monogenic free inverse semigroup
• Anisimov's Theorem for inverse semigroups
• Inverse subsemigroups of finite index in finitely generated inverse semigroups
• Some conditions from a finite regular semigroup to a finite inverse semigroup
• Regular semigroups weakly generated by idempotents