The Menger algebra of terms induced by order-decreasing transformations

Let tau(n) be a type of algebras with the n-ary operation symbols, for a fixed integer n >= 1. In this article, we introduce terms of type tau(n) called order-decreasing full terms. We prove that the set of all order-decreasing full terms of type tau(n) is closed under the superposition operation; and hence it forms an algebra denoted by MA(ODn)(tau(n)). Moreover, we prove that MA(ODn) (tau(n)) is a Menger algebra of rank n. Finally, we introduce and study order-decreasing full hypersubstitutions and the related order-decreasing full closed identities and order-decreasing full closed varieties.