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arXiv · 2403.06957

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

Apatsara Sareeto·Jörg Koppitz
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Abstract

In the present paper, a submonoid of the well studied monoid $POI_n$ of all order-preserving partial injections on an $n$-element chain is studied. The set $IOF_n^{par}$ of all partial transformations in $POI_n$ which are fence-preserving as well as parity-preserving form a submonoid of $POI_n$. We describe the Green's relations and ideals of $IOF_n^{par}$. For each ideal of $IOF_n^{par}$, we characterize the maximal subsemigroups. We will observe that there are three different types of maximal subsemigroups.

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Apatsara Sareeto, Jörg Koppitz. 2024-03-11. The maximal subsemigroups of the ideals on a monoid of partial injections. https://arxiv.org/abs/2403.06957

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