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

Ampika Boonmee, Sorasak Leeratanavalee

Abstract

A generalized hypersubstitution of type $\tau$ maps any operation symbol to the set of all terms of the same type which does not necessarily preserve the arity. Every generalized hypersubstitution can be extended to a mapping on the set of all terms. We define a binary operation on the set of all generalized hypersubstitutions by using this extension. It turns out that this set together with the binary operation forms a monoid. In this paper, we characterize all unit elements and determine the set of all unit regular elements of this monoid of type  $\tau = (2)$. We conclude a submonoid of the moniod of all generalized hypersubstitutions of type  $\tau = (2)$ which is factorisable.