Natural partial order on semigroups of partial transformations with invariant set

• Date: 2026
• Main Authors: Srisawat, Jitsupa, Chaiya, Yanisa
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: partial transformation semigroups; partial orders; compatible elements; minimal and maximal elements; 20M20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2434
• Journal Title: Algebra and Discrete Mathematics

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 \(...