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

Apatsara Sareeto; Jörg Koppitz

paper

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

arXiv:2403.06957

Abstract

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

12 pages