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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| Main Authors: | , |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2024-03-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/476 |
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| Summary: | 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. |
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| ISSN: | 1027-4634 2411-0620 |