The inverse semigroup of all fence-preserving injections and its maximal subsemigroups
In this paper, we study the inverse semigroup \(IF_{n}\) of all partial injections \(\alpha\) on an \(n\)-element set such that both \(\alpha\) and \(\alpha^{-1}\) are fence-preserving (preserve the zig-zag order). The main result of this paper is the characterization of the maximal subsemigroups of...
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Lugansk National Taras Shevchenko University
2025
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oai:ojs.admjournal.luguniv.edu.ua:article-23532025-08-13T10:04:13Z The inverse semigroup of all fence-preserving injections and its maximal subsemigroups Passararat, Boonnisa Koppitz, Jörg partial transformations, fence-preserving, inverse semigroup, maximal subsemigroups 20M20, 20M10 In this paper, we study the inverse semigroup \(IF_{n}\) of all partial injections \(\alpha\) on an \(n\)-element set such that both \(\alpha\) and \(\alpha^{-1}\) are fence-preserving (preserve the zig-zag order). The main result of this paper is the characterization of the maximal subsemigroups of \(IF_{n}\): There are five types of maximal subsemigroups, whenever \(n\) is odd; if \(n\) is even, then the maximal semigroups are of the form \(IF_{n}\setminus \{\alpha \}\), where \(\alpha\) belongs to the least generating set of \(IF_{n}\). Moreover, we describe the i-conjugate elements in \(IF_{n}\). Lugansk National Taras Shevchenko University 2025-08-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2353 10.12958/adm2353 Algebra and Discrete Mathematics; Vol 39, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2353/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2353/1264 Copyright (c) 2025 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2025-08-13T10:04:13Z |
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OJS |
| language |
English |
| topic |
partial transformations fence-preserving inverse semigroup maximal subsemigroups 20M20 20M10 |
| spellingShingle |
partial transformations fence-preserving inverse semigroup maximal subsemigroups 20M20 20M10 Passararat, Boonnisa Koppitz, Jörg The inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| topic_facet |
partial transformations fence-preserving inverse semigroup maximal subsemigroups 20M20 20M10 |
| format |
Article |
| author |
Passararat, Boonnisa Koppitz, Jörg |
| author_facet |
Passararat, Boonnisa Koppitz, Jörg |
| author_sort |
Passararat, Boonnisa |
| title |
The inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| title_short |
The inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| title_full |
The inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| title_fullStr |
The inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| title_full_unstemmed |
The inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| title_sort |
inverse semigroup of all fence-preserving injections and its maximal subsemigroups |
| description |
In this paper, we study the inverse semigroup \(IF_{n}\) of all partial injections \(\alpha\) on an \(n\)-element set such that both \(\alpha\) and \(\alpha^{-1}\) are fence-preserving (preserve the zig-zag order). The main result of this paper is the characterization of the maximal subsemigroups of \(IF_{n}\): There are five types of maximal subsemigroups, whenever \(n\) is odd; if \(n\) is even, then the maximal semigroups are of the form \(IF_{n}\setminus \{\alpha \}\), where \(\alpha\) belongs to the least generating set of \(IF_{n}\). Moreover, we describe the i-conjugate elements in \(IF_{n}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2353 |
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AT passararatboonnisa theinversesemigroupofallfencepreservinginjectionsanditsmaximalsubsemigroups AT koppitzjorg theinversesemigroupofallfencepreservinginjectionsanditsmaximalsubsemigroups AT passararatboonnisa inversesemigroupofallfencepreservinginjectionsanditsmaximalsubsemigroups AT koppitzjorg inversesemigroupofallfencepreservinginjectionsanditsmaximalsubsemigroups |
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2025-09-17T09:26:10Z |
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2025-09-17T09:26:10Z |
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