Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree
This paper deals with a semigroup of order-decreasing transformations of a rooted tree. Such are the transformations \(\alpha\) of some rooted tree \(G\) satisfying following condition: for any \(x\) from \(G\) \(\alpha(x)\) belongs to a simple path from \(x\) to the root vertex of \(G\). We descri...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/911 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543441857544192 |
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| author | Stronska, Anna |
| author_facet | Stronska, Anna |
| author_sort | Stronska, Anna |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T07:55:00Z |
| description | This paper deals with a semigroup of order-decreasing transformations of a rooted tree. Such are the transformations \(\alpha\) of some rooted tree \(G\) satisfying following condition: for any \(x\) from \(G\) \(\alpha(x)\) belongs to a simple path from \(x\) to the root vertex of \(G\). We describe all subsemigroups of the mentioned semigroup, which are maximal among nilpotent subsemigroups of nilpotency class \(k\) in our semigroup. In the event when rooted tree is a ray we prove that all these maximal subsemigroups are pairwise nonisomorphic. |
| first_indexed | 2025-12-02T15:43:35Z |
| format | Article |
| id | admjournalluguniveduua-article-911 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:35Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9112018-03-21T07:55:00Z Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree Stronska, Anna semigroup, order-decreasing, non-isomorphic 20M20 This paper deals with a semigroup of order-decreasing transformations of a rooted tree. Such are the transformations \(\alpha\) of some rooted tree \(G\) satisfying following condition: for any \(x\) from \(G\) \(\alpha(x)\) belongs to a simple path from \(x\) to the root vertex of \(G\). We describe all subsemigroups of the mentioned semigroup, which are maximal among nilpotent subsemigroups of nilpotency class \(k\) in our semigroup. In the event when rooted tree is a ray we prove that all these maximal subsemigroups are pairwise nonisomorphic. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/911 Algebra and Discrete Mathematics; Vol 5, No 4 (2006) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/911/440 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | semigroup order-decreasing non-isomorphic 20M20 Stronska, Anna Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| title | Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| title_full | Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| title_fullStr | Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| title_full_unstemmed | Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| title_short | Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| title_sort | nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree |
| topic | semigroup order-decreasing non-isomorphic 20M20 |
| topic_facet | semigroup order-decreasing non-isomorphic 20M20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/911 |
| work_keys_str_mv | AT stronskaanna nilpotentsubsemigroupsofasemigroupoforderdecreasingtransformationsofarootedtree |