Boolean-like-algebras

Using Vaggione's concept of central element in a double-pointed algebra, we introduce the notion of \emph{Boolean-like variety} as a generalisation of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of \emph{semi-Boolean-like varieties}, which still retain many of the pleasing properties of Boolean algebras. We prove that a double-pointed variety is discriminator iff it is semi-Boolean-like, idempotent, and $0$-regular. This theorem yields a new Maltsev-style characterisation of double-pointed discriminator varieties.