Factorisable Monoid of Generalized Cohypersubstitutions of Type $\tau=(2)$

Nagornchat Chansuriya, Sarawut Phuapong

Abstract

Generalized cohypersubstitutions of type $\tau = (n_{i})_{i \in I}$ are mappings which send $n_{i}$-ary cooperation symbols to coterms of type $\tau$. Every  generalized cohypersubstitution can be extended to a mapping on the set of all coterms. We define a binary operation on the set of all generalized cohypersubstitutions by using this extension. In this paper, we characterize all unit elements and determine the set of all unit-regular elements of this monoid of type $\tau = (2)$. Finally, a submonoid of the monoid of all generalized hypersubstitutions of type $\tau = (2)$ which is factorisable is presented.