Factorisable monoid of generalized hypersubstitutions of type Γ = (2)

Abstract

© 2015 by the Mathematical Association of Thailand. All rights reserved. A generalized hypersubstitution of type Γ 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 Γ = (2). We conclude a submonoid of the moniod of all generalized hypersubstitutions of type Γ = (2) which is factorisable.