Natural partial order on semigroups of partial transformations with invariant set
Let \(X\) be a non-empty set, and let \(P(X)\) denote the semigroup of partial transformations on \(X\). For a non-empty subset \(Y\) of \(X\), define \(\overline{PT}(X,Y) = \{\alpha \in P(X) \mid (\text{dom } \alpha \cap Y)\alpha \subseteq Y \}.\) The semigroup \(\overline{PT}(X,Y)\) generalizes \(...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2026
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2434 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | Let \(X\) be a non-empty set, and let \(P(X)\) denote the semigroup of partial transformations on \(X\). For a non-empty subset \(Y\) of \(X\), define \(\overline{PT}(X,Y) = \{\alpha \in P(X) \mid (\text{dom } \alpha \cap Y)\alpha \subseteq Y \}.\) The semigroup \(\overline{PT}(X,Y)\) generalizes \(P(X)\) and consists of all partial transformations on \(X\) that leave \(Y\) invariant. In this paper, we investigate the natural partial order on \(\overline{PT}(X,Y)\) and characterize its left-compatible, right-compatible, minimal, and maximal elements. The results obtained extend and unify several known properties of \(P(X).\) |
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| DOI: | 10.12958/adm2434 |