Amalgamation in varieties of distributive double \(p\)-algebras (Q1342127)

The authors show that the variety \(A\) of all distributive \(p\)-algebras and its subvariety \(R\) of regular double \(p\)-algebras have the amalgamation property, and augment results of Banaschewski, Katriňák and others to a characterization of finitely generated varieties of distributive double \(p\)-algebras which have the AP. They also describe all subvarieties \(V\) of \(V^{(n)}\) or \(V_{(n)}\) with the AP, and show that if regular, such a variety has the AP exactly when it is generated by a max-homogeneous or a min-homogeneous algebra. They also show that many varieties of distributive double \(p\)-algebras have non- surjective epimorphisms.