All Maximal Idempotent Submonoids of Generalized Cohypersubstitutions of Type τ = (2)

Abstract

Abstract A generalized cohypersubstitution of type τ is a mapping σ which maps every ni-ary cooperation symbol fi to the coterm σ(f ) of type τ = (ni)i∈I. Denote by CohypG(τ) the set of all generalized cohypersubstitutions of type τ. Define the binary operation ◦CG on CohypG(τ) by σ1◦CG σ2:= σ ˆ1 ◦ σ2 for all σ1, σ2 ∈ CohypG(τ) and σid(fi) := fi for all i ∈ I. Then CohypG(τ) := {CohypG(τ), ◦CG, σid} is a monoid. In [5], the monoid CohypG(2) was studied. They characterized and presented the idempotent and regular elements of this monoid. In this present paper, we consider the set of all idempotent elements of the monoid CohypG(2) and determine all maximal idempotent submonoids of this monoid.