Monogenic free inverse semigroups and partial automorphisms of regular rooted trees
For a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free inverse. We also give a sufficient condition for a regular rooted tree partial automorphism to extend to...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2024-03-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/476 |
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| author | E. Kochubinska A. Oliynyk |
| author_facet | E. Kochubinska A. Oliynyk |
| author_sort | E. Kochubinska |
| collection | DOAJ |
| description | For a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free inverse.
We also give a sufficient condition for a regular rooted tree partial automorphism to extend to a partial automorphism of another regular rooted tree so that the inverse semigroup gene\-ra\-ted by this extended partial automorphism is monogenic free inverse. The extension procedure we develop is then applied to $n$-ary adding machines. |
| format | Article |
| id | doaj-art-0f20a17df2044b4e9bc25b7b3c197d85 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2024-03-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-0f20a17df2044b4e9bc25b7b3c197d852025-08-20T03:28:21ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202024-03-016113910.30970/ms.61.1.3-9476Monogenic free inverse semigroups and partial automorphisms of regular rooted treesE. Kochubinska0A. Oliynyk1Taras Shevchenko National University Kyiv UkraineTaras Shevchenko National University Kyiv UkraineFor a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free inverse. We also give a sufficient condition for a regular rooted tree partial automorphism to extend to a partial automorphism of another regular rooted tree so that the inverse semigroup gene\-ra\-ted by this extended partial automorphism is monogenic free inverse. The extension procedure we develop is then applied to $n$-ary adding machines.http://matstud.org.ua/ojs/index.php/matstud/article/view/476free inverse semigroup;rooted tree; partial automorphism |
| spellingShingle | E. Kochubinska A. Oliynyk Monogenic free inverse semigroups and partial automorphisms of regular rooted trees Математичні Студії free inverse semigroup; rooted tree; partial automorphism |
| title | Monogenic free inverse semigroups and partial automorphisms of regular rooted trees |
| title_full | Monogenic free inverse semigroups and partial automorphisms of regular rooted trees |
| title_fullStr | Monogenic free inverse semigroups and partial automorphisms of regular rooted trees |
| title_full_unstemmed | Monogenic free inverse semigroups and partial automorphisms of regular rooted trees |
| title_short | Monogenic free inverse semigroups and partial automorphisms of regular rooted trees |
| title_sort | monogenic free inverse semigroups and partial automorphisms of regular rooted trees |
| topic | free inverse semigroup; rooted tree; partial automorphism |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/476 |
| work_keys_str_mv | AT ekochubinska monogenicfreeinversesemigroupsandpartialautomorphismsofregularrootedtrees AT aoliynyk monogenicfreeinversesemigroupsandpartialautomorphismsofregularrootedtrees |