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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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua: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 |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-05-15T06:58:22Z |
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English |
| topic |
Clone unitary Menger algebra of type \(\tau_n\) full hyperidentity n-F-solid variety 08A40 08A60 08A02 20M35 |
| 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 |
| topic_facet |
Clone unitary Menger algebra of type \(\tau_n\) full hyperidentity n-F-solid variety 08A40 08A60 08A02 20M35 |
| format |
Article |
| author |
Denecke, Klaus Jampachon, Prakit |
| author_facet |
Denecke, Klaus Jampachon, Prakit |
| author_sort |
Denecke, Klaus |
| title |
Clones of full terms |
| title_short |
Clones of full terms |
| title_full |
Clones of full terms |
| title_fullStr |
Clones of full terms |
| title_full_unstemmed |
Clones of full terms |
| title_sort |
clones of full terms |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1007 |
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AT deneckeklaus clonesoffullterms AT jampachonprakit clonesoffullterms |
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2025-07-17T10:33:11Z |
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2025-07-17T10:33:11Z |
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