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).