Geodesic
On finite presentability of subsemigroups of the monogenic free inverse semigroup
Glasgow mathematical journal, Tome 67 (2025) no. 2, pp. 185-196

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DOI

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.
DOI : 10.1017/S0017089524000314
Mots-clés : Free inverse semigroup, monogenic, subsemigroup, finite presentation, idempotents 
Cho, Jung Won; Ruškuc, Nik. On finite presentability of subsemigroups of the monogenic free inverse semigroup. Glasgow mathematical journal, Tome 67 (2025) no. 2, pp. 185-196. doi: 10.1017/S0017089524000314
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     title = {On finite presentability of subsemigroups of the monogenic free inverse semigroup},
     journal = {Glasgow mathematical journal},
     pages = {185--196},
     year = {2025},
     volume = {67},
     number = {2},
     doi = {10.1017/S0017089524000314},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000314/}
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