Clones of full terms

Abstract

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 IdF n V of all its identities built up by full n-ary terms forms a congruence relation on that Menger algebra. If IdF n V 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.