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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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2026
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| 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| _version_ | 1861680840586559488 |
|---|---|
| author | Srisawat, Jitsupa Chaiya, Yanisa |
| author_facet | Srisawat, Jitsupa Chaiya, Yanisa |
| author_sort | Srisawat, Jitsupa |
| baseUrl_str | https://admjournal.luguniv.edu.ua/index.php/adm/oai |
| collection | OJS |
| datestamp_date | 2026-04-05T09:02:49Z |
| description | 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 \(P(X).\) |
| doi_str_mv | 10.12958/adm2434 |
| first_indexed | 2026-04-06T01:00:02Z |
| format | Article |
| id | admjournalluguniveduua-article-2434 |
| institution | Algebra and Discrete Mathematics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-06T01:00:02Z |
| publishDate | 2026 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-24342026-04-05T09:02:49Z Natural partial order on semigroups of partial transformations with invariant set Srisawat, Jitsupa Chaiya, Yanisa partial transformation semigroups, partial orders, compatible elements, minimal and maximal elements 20M20 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 \(P(X).\) Lugansk National Taras Shevchenko University 2026-04-05 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2434 10.12958/adm2434 Algebra and Discrete Mathematics; Vol 41, No 1 (2026) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2434/pdf Copyright (c) 2026 Algebra and Discrete Mathematics |
| spellingShingle | partial transformation semigroups partial orders compatible elements minimal and maximal elements 20M20 Srisawat, Jitsupa Chaiya, Yanisa Natural partial order on semigroups of partial transformations with invariant set |
| title | Natural partial order on semigroups of partial transformations with invariant set |
| title_full | Natural partial order on semigroups of partial transformations with invariant set |
| title_fullStr | Natural partial order on semigroups of partial transformations with invariant set |
| title_full_unstemmed | Natural partial order on semigroups of partial transformations with invariant set |
| title_short | Natural partial order on semigroups of partial transformations with invariant set |
| title_sort | natural partial order on semigroups of partial transformations with invariant set |
| topic | partial transformation semigroups partial orders compatible elements minimal and maximal elements 20M20 |
| topic_facet | partial transformation semigroups partial orders compatible elements minimal and maximal elements 20M20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2434 |
| work_keys_str_mv | AT srisawatjitsupa naturalpartialorderonsemigroupsofpartialtransformationswithinvariantset AT chaiyayanisa naturalpartialorderonsemigroupsofpartialtransformationswithinvariantset |