The structures of full terms preserving a partition under different operations

Full terms that preserve a partition in a finite set are extension of full terms, which can be applied to classify algebras of the same type into subclasses known as the full solid variety preserving a partition. In this paper, two associative binary operations induced by a superassociative superposition defined on the set of full terms preserving a partition are given. As a generalization, sets of such full terms and their binary operations are also discussed.