On mappings of terms determined by hypersubstitutions
The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid.On the other hand, one can modify each hypersubstitution to a...
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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/925 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543410561744896 |
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| author | Koppitz, Jorg Shtrakov, Slavcho |
| author_facet | Koppitz, Jorg Shtrakov, Slavcho |
| author_sort | Koppitz, Jorg |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T06:47:49Z |
| description | The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid.On the other hand, one can modify each hypersubstitution to any mapping on the set of terms. For this we can consider mappings \(\rho \) from the set of all hypersubstitutions into the set of all mappings on the set of all terms. If for each hypersubstitution \(\sigma \) the application of \(\rho (\sigma )\) to any identity in a given variety \(V\) is again an identity in \(V\), so that variety is called \(\rho \)-solid. The concept of a \(\rho \)-solid variety generalizes the concept of a solid variety. In the present paper, we determine all \(\rho \)-solid varieties of semigroups for particular mappings \( \rho \). |
| first_indexed | 2025-12-02T15:41:28Z |
| format | Article |
| id | admjournalluguniveduua-article-925 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:28Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9252018-03-21T06:47:49Z On mappings of terms determined by hypersubstitutions Koppitz, Jorg Shtrakov, Slavcho \(\rho\)-solid, hypersubstitution, bijection 20M14, 20M07 The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid.On the other hand, one can modify each hypersubstitution to any mapping on the set of terms. For this we can consider mappings \(\rho \) from the set of all hypersubstitutions into the set of all mappings on the set of all terms. If for each hypersubstitution \(\sigma \) the application of \(\rho (\sigma )\) to any identity in a given variety \(V\) is again an identity in \(V\), so that variety is called \(\rho \)-solid. The concept of a \(\rho \)-solid variety generalizes the concept of a solid variety. In the present paper, we determine all \(\rho \)-solid varieties of semigroups for particular mappings \( \rho \). 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/925 Algebra and Discrete Mathematics; Vol 4, No 3 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/925/454 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | \(\rho\)-solid hypersubstitution bijection 20M14 20M07 Koppitz, Jorg Shtrakov, Slavcho On mappings of terms determined by hypersubstitutions |
| title | On mappings of terms determined by hypersubstitutions |
| title_full | On mappings of terms determined by hypersubstitutions |
| title_fullStr | On mappings of terms determined by hypersubstitutions |
| title_full_unstemmed | On mappings of terms determined by hypersubstitutions |
| title_short | On mappings of terms determined by hypersubstitutions |
| title_sort | on mappings of terms determined by hypersubstitutions |
| topic | \(\rho\)-solid hypersubstitution bijection 20M14 20M07 |
| topic_facet | \(\rho\)-solid hypersubstitution bijection 20M14 20M07 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/925 |
| work_keys_str_mv | AT koppitzjorg onmappingsoftermsdeterminedbyhypersubstitutions AT shtrakovslavcho onmappingsoftermsdeterminedbyhypersubstitutions |