De Sole, AlbertoKac, Victor G.Valeri, Daniele2014-01-312014-01-312014-01https://openscience.sissa.it/handle/1963/724715 pagesFirst, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.enPreprintMAT/07 FISICA MATEMATICA