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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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1007 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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