Green's Relations on HypG(2)

A generalized hypersubstitution of type τ = (2) is a mapping which maps the binary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ = (2), and any two such extensions can be composed in a natural way. Thus, the set HypG(2) of all generalized hypersubstitutions of type τ = (2) forms a monoid. Green's relations on the monoid of all hypersubstitutions of type τ = (2) were studied by K. Denecke and Sh.L. Wismath. In this paper we describe the classes of generalized hypersubstitutions of type τ = (2) under Green's relations.