Boolean powers were introduced by Foster [5]. It was noticed by Jónsson in the review of [6], and further elaborated by Banaschewski and Nelson [1], that the Boolean power of an algebra A by a Boolean algebra B can be described as the algebra of continuous functions from the Stone space of B to A, where A has the discrete topology. It follows that a Boolean power of the group Z is an `-group ge...

In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras a...