Clones of full terms
In this paper the well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied in a restricted setting, that of \(n\)-ary full hyperidentities and identities of the \(n\)-ary clone of term operations which are induced by full terms. We...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1007 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543415093690368 |
|---|---|
| author | Denecke, Klaus Jampachon, Prakit |
| author_facet | Denecke, Klaus Jampachon, Prakit |
| author_sort | Denecke, Klaus |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-15T06:58:22Z |
| description | In this paper the well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied in a restricted setting, that of \(n\)-ary full hyperidentities and identities of the \(n\)-ary clone of term operations which are induced by full terms. We prove that the \(n\)-ary full terms form an algebraic structure which is called a Menger algebra of rank \(n\). For a variety \(V\), the set \(Id_n^FV\) of all its identities built up by full \(n\)-ary terms forms a congruence relation on that Menger algebra. If \(Id_n^FV\) is closed under all full hypersubstitutions, then the variety \(V\) is called \(n-F-\)solid. We will give a characterization of such varieties and apply the results to \(2-F-\)solid varieties of commutative groupoids. |
| first_indexed | 2025-12-02T15:41:40Z |
| format | Article |
| id | admjournalluguniveduua-article-1007 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:40Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-10072018-05-15T06:58:22Z Clones of full terms Denecke, Klaus Jampachon, Prakit Clone, unitary Menger algebra of type \(\tau_n\), full hyperidentity, n-F-solid variety 08A40, 08A60, 08A02, 20M35 In this paper the well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied in a restricted setting, that of \(n\)-ary full hyperidentities and identities of the \(n\)-ary clone of term operations which are induced by full terms. We prove that the \(n\)-ary full terms form an algebraic structure which is called a Menger algebra of rank \(n\). For a variety \(V\), the set \(Id_n^FV\) of all its identities built up by full \(n\)-ary terms forms a congruence relation on that Menger algebra. If \(Id_n^FV\) is closed under all full hypersubstitutions, then the variety \(V\) is called \(n-F-\)solid. We will give a characterization of such varieties and apply the results to \(2-F-\)solid varieties of commutative groupoids. Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1007 Algebra and Discrete Mathematics; Vol 3, No 4 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1007/536 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Clone unitary Menger algebra of type \(\tau_n\) full hyperidentity n-F-solid variety 08A40 08A60 08A02 20M35 Denecke, Klaus Jampachon, Prakit Clones of full terms |
| title | Clones of full terms |
| title_full | Clones of full terms |
| title_fullStr | Clones of full terms |
| title_full_unstemmed | Clones of full terms |
| title_short | Clones of full terms |
| title_sort | clones of full terms |
| topic | Clone unitary Menger algebra of type \(\tau_n\) full hyperidentity n-F-solid variety 08A40 08A60 08A02 20M35 |
| topic_facet | Clone unitary Menger algebra of type \(\tau_n\) full hyperidentity n-F-solid variety 08A40 08A60 08A02 20M35 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1007 |
| work_keys_str_mv | AT deneckeklaus clonesoffullterms AT jampachonprakit clonesoffullterms |