The Amalgamation Property in the Variety of Regular Double Stone Algebras: A Constructive View

In this paper we give a constructive proof that the variety of Boolean algebras has the strong amalgamation property by describing constructively the strong amalgams in the variety. Then, capitalizing on this construction, we investigate several forms of amalgamation, such as the strong amalgamation property and Maksimova super-amalgamation for the varieties of regular double Stone algebras and centered regular double Stone algebras. In fact, we prove that the amalgamation property holds for the variety RDS. Then, we introduce the variety RDSk of centered regular double Stone algebras and prove that RDSk enjoys the strong amalgamation property. It is also proved that the varieties of Boolean algebras and centered regular double Stone algebras have the super-amalgamation property. We close the paper by providing a number of concrete examples and applications to illustrate the theory developed in the paper.