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

Abstract

A mapping [Formula: see text] from [Formula: see text], the set of all co-operation symbols of type [Formula: see text], into [Formula: see text], the set of all coterms of type [Formula: see text], is said to be a generalized cohypersubstitution of type [Formula: see text]. Every generalized cohypersubstition [Formula: see text] of type [Formula: see text] induces a mapping [Formula: see text] on the set of all coterms of type [Formula: see text]. The set of all generalized cohypersubstitutions of type [Formula: see text], [Formula: see text], under the binary operation [Formula: see text], which is defined by [Formula: see text] for all [Formula: see text], forms a monoid which is called the monoid of generalized cohypersubstitution of type [Formula: see text]. In this research, we characterize all idempotent and regular elements of [Formula: see text], where [Formula: see text].