IDEMPOTENT ELEMENTS OF PRE-GENERALIZED HYPERSUBSTITUTIONS OF TYPE (m, n)

Abstract

A generalized hypersubstitution of type τ = (m, n) is a mapping σ which maps the m-ary operation symbol f and n-ary operation symbol g to the term σ(f) and σ(g), and may not preserved arities.  Each generalized hypersubstitution can be extended to a mapping \(\hat{σ}\) on the set of all terms of type τ = (m, n). The structure (Hyp_G(τ ); ◦_G, σ_id) is a monoid where σ_id is an identity hypersubstitution.  A pregeneralized hypersubstitution of type τ = (m, n), namely σ, is a generalized hypersubstitution of type τ = (m, n) where σ(f) and σ(g) are not variables.  In this paper, we characterize idempotent pre-generalized hypersubstitutions of type τ = (m, n).