Geodesic
Clones of full terms
Algebra and discrete mathematics, no. 4 (2004), pp. 1-11

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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.
Keywords: Clone, unitary Menger algebra of type $\tau_n$, full hyperidentity, $n-F$-solid variety. 
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     author = {Klaus Denecke and Prakit Jampachon},
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Klaus Denecke; Prakit Jampachon. Clones of full terms. Algebra and discrete mathematics, no. 4 (2004), pp. 1-11. http://geodesic.mathdoc.fr/item/ADM_2004_4_a0/