Simple weakly transitive modal algebras

Weakly transitive modal algebras are studied. It is proved that the class of simple weakly transitive algebras coincides with the class of simple $DL$-algebras. A full description is given for finitely generated simple $DL$-algebras together with their embeddings. As a consequence, it is shown that the varieties of weakly transitive algebras and of $DL$-algebras are not weakly amalgamable, and that modal logics $wK4$ and $DL$ do not possess the weak interpolation property.