Factorisable monoid of generalized hypersubstitutions of type \tau =(n)

Abstract

A generalized hypersubstitution of type \tau maps any  operation symbols to the set of all terms. The extensions of generalized hypersubstitutions are mappings on the set of all terms. The set of all such generalized hypersubstitutions forms a monoid. In this paper we determine the set of all unit-regular elements of this monoid of type \tau=(n).  We also conclude a submonoid of the monoid of all generalized hypersubstitutions of type \tau=(n) which is factorisable.