Green’s Relations on Submonoids of Generalized Hypersubstitutions of Type (n)

Abstract A generalized hypersubstitution of type τ = (n) is a function which takes the n-ary operation symbol f to the term of the same type σ(f ) which does not necessarily preserve the arity. Let HypG(n) be the set of all these generalized hypersubstitutions of type (n). The set HypG(n) with a binary operation and the identity generalized hypersubstitution forms a monoid. The objective of this paper is to study Green’s relations on the set of all regular elements of HypG(n).