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: | English |
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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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oai:ojs.admjournal.luguniv.edu.ua: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 |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2024-06-27T08:42:43Z |
| collection |
OJS |
| language |
English |
| topic |
partial (full) transformations semigroup quasi-idempotent orbit rank 20M20 |
| spellingShingle |
partial (full) transformations semigroup quasi-idempotent orbit rank 20M20 Bugay, Leyla Quasi-idempotents in certain transformation semigroups |
| topic_facet |
partial (full) transformations semigroup quasi-idempotent orbit rank 20M20 |
| format |
Article |
| author |
Bugay, Leyla |
| author_facet |
Bugay, Leyla |
| author_sort |
Bugay, Leyla |
| title |
Quasi-idempotents in certain transformation semigroups |
| title_short |
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_sort |
quasi-idempotents in certain transformation semigroups |
| 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 \(\alpha\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2223 |
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AT bugayleyla quasiidempotentsincertaintransformationsemigroups |
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2024-06-28T04:03:55Z |
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2024-06-28T04:03:55Z |
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