The maximal subsemigroups of the ideals in a monoid of partial injections

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2024年5月31日

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Apatsara Sareeto,
Jörg Koppitz

摘要

We study a submonoid of the well studied monoid $POI_n$ $P O I_{n}$ of all order-preserving partial injections on an n-element chain. The set $IOF_n^{par}$ $I O F_{n}^{par}$ of all partial transformations in $POI_n$ $P O I_{n}$ which are fence-preserving as well as parity-preserving forms a submonoid of $POI_n$ $P O I_{n}$ . We describe Green’s relations and ideals of $IOF_n^{par}$ $I O F_{n}^{par}$ . For each ideal of $IOF_n^{par}$ $I O F_{n}^{par}$ , we characterize the maximal subsemigroups. We observe that there are three different types of maximal subsemigroups.