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 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.