Idempotent and regular in monoid of generalized cohypersubstitutions of type τ = (3)

摘要

A mapping σ from {?_i | i ∈ I}，the set of all co-operation symbols of type τ, into CT_T, the set of all coterms of type τ, is said to be a generalized cohypersubstitution of type τ. Every generalized cohypersubstition σ of type r induces a mapping σ on the set of all coterms of type τ. The set of all generalized cohypersubstitutions of type τ, Cohyp_G (r), under the binary operation o_(CG), which is defined by σ_1 o_(CG) σ_2：= σ_1 o σ_2 for all σ_1, σ_2 ∈ Cohyp_G(τ)， forms a monoid which is called the monoid of generalized cohypersubstitution of type r. In this research, we characterize all idempotent and regular elements of Cohyp_G(τ), where r = (3).