On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913524336295936 |
|---|---|
| author | Cho, Yung Won Ruskuc, Nik |
| author_facet | Cho, Yung Won Ruskuc, Nik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup Cho, Yung Won Ruskuc, Nik Group Theory 20M05, 20M18 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. |
| title | On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup |
| topic | Group Theory 20M05, 20M18 |
| url | https://arxiv.org/abs/2404.05244 |