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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.06957 |
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| _version_ | 1866914709617246208 |
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| author | Sareeto, Apatsara Koppitz, Jörg |
| author_facet | Sareeto, Apatsara Koppitz, Jörg |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximal subsemigroups of the ideals on a monoid of partial injections Sareeto, Apatsara Koppitz, Jörg Rings and Algebras 20M12, 20M18, 20M20 F.4.1 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. |
| title | The maximal subsemigroups of the ideals on a monoid of partial injections |
| topic | Rings and Algebras 20M12, 20M18, 20M20 F.4.1 |
| url | https://arxiv.org/abs/2403.06957 |