Notes on bounded Hilbert algebras with supremum

Abstract

In this note we will investigate some particular classes of ideals in Hilbert algebras with supremum. We shall study the relation between -ideals and annihilator ideals in bounded Hilbert algebras with supremum. We shall introduce the class of -ideals and we will see that this class is strongly connected with the deductive systems. We will also characterize the bounded Hilbert algebras with supremum satisfying the Stone identity.