Defining an (n+1)-ary superposition operation $S^n$ on the set $W_{\tau }\left(X_n\right)$ of all n-ary terms of type τ, one obtains an algebra $n-clone\tau :=(W_{\tau }\left(X_n\right);S^n,x_1,...,x_n)$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^n$ there are different possibilities to define binary associative operations on the set $W_{\tau }\left(X_n\right)$ and on the cartesian power $W_{\tau }{\left(X_n\right)}^n$. In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative operations...

A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a₁,a₂,...,aₙ of X implies f(p(a₁),p(a₂),...,p(aₙ)) = g(p(a₁),p(a₂),...,p(aₙ)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). We investigate Q-independent subsets of algebras which have a retraction in their set of term functions.