Quasi-idempotents in certain transformation semigroups
Let \(P_{n}\) and \(T_{n}\) be the partial transformations semigroup and the (full) transformations semigroup on the set \(X_{n}=\{1,\ldots ,n\}\), respectively. In this paper, we first state the orbit structure of quasi-idempotents (non-idempotent element whose square is an idempotent) in \(P_{n}\)...
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| Дата: | 2024 |
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| Формат: | Стаття |
| Мова: | Англійська |
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Lugansk National Taras Shevchenko University
2024
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2223 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543250383372288 |
|---|---|
| author | Bugay, Leyla |
| author_facet | Bugay, Leyla |
| author_sort | Bugay, Leyla |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2024-06-27T08:42:43Z |
| description | Let \(P_{n}\) and \(T_{n}\) be the partial transformations semigroup and the (full) transformations semigroup on the set \(X_{n}=\{1,\ldots ,n\}\), respectively. In this paper, we first state the orbit structure of quasi-idempotents (non-idempotent element whose square is an idempotent) in \(P_{n}\). Then, for \(2\leq r\leq n-1\), we find the quasi-idempotent ranks of the subsemigroup \(PK(n,r)=\{\alpha \in P_{n}: \mathrm{h}(\alpha) \leq r\}\) of \(P_{n}\), and the subsemigroup \(K(n,r)=\{\alpha \in T_{n}: \mathrm{h}(\alpha) \leq r\}\) of \(T_{n}\), where \(\mathrm{h}(\alpha)\) denotes the cardinality of the image set of \(\alpha\). |
| first_indexed | 2026-02-08T08:00:14Z |
| format | Article |
| id | admjournalluguniveduua-article-2223 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:00:14Z |
| publishDate | 2024 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-22232024-06-27T08:42:43Z Quasi-idempotents in certain transformation semigroups Bugay, Leyla partial (full) transformations semigroup, quasi-idempotent, orbit, rank 20M20 Let \(P_{n}\) and \(T_{n}\) be the partial transformations semigroup and the (full) transformations semigroup on the set \(X_{n}=\{1,\ldots ,n\}\), respectively. In this paper, we first state the orbit structure of quasi-idempotents (non-idempotent element whose square is an idempotent) in \(P_{n}\). Then, for \(2\leq r\leq n-1\), we find the quasi-idempotent ranks of the subsemigroup \(PK(n,r)=\{\alpha \in P_{n}: \mathrm{h}(\alpha) \leq r\}\) of \(P_{n}\), and the subsemigroup \(K(n,r)=\{\alpha \in T_{n}: \mathrm{h}(\alpha) \leq r\}\) of \(T_{n}\), where \(\mathrm{h}(\alpha)\) denotes the cardinality of the image set of \(\alpha\). Lugansk National Taras Shevchenko University 2024-06-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2223 10.12958/adm2223 Algebra and Discrete Mathematics; Vol 37, No 2 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2223/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2223/1158 Copyright (c) 2024 Algebra and Discrete Mathematics |
| spellingShingle | partial (full) transformations semigroup quasi-idempotent orbit rank 20M20 Bugay, Leyla Quasi-idempotents in certain transformation semigroups |
| title | Quasi-idempotents in certain transformation semigroups |
| title_full | Quasi-idempotents in certain transformation semigroups |
| title_fullStr | Quasi-idempotents in certain transformation semigroups |
| title_full_unstemmed | Quasi-idempotents in certain transformation semigroups |
| title_short | Quasi-idempotents in certain transformation semigroups |
| title_sort | quasi-idempotents in certain transformation semigroups |
| topic | partial (full) transformations semigroup quasi-idempotent orbit rank 20M20 |
| topic_facet | partial (full) transformations semigroup quasi-idempotent orbit rank 20M20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2223 |
| work_keys_str_mv | AT bugayleyla quasiidempotentsincertaintransformationsemigroups |