  We develop a new method for constructing integrable Hamiltonian hierarchies
of Lax type equations, which combines the fractional powers technique of
Gelfand and Dickey, and the classical Hamiltonian reduction technique of
Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix
pseudodifferential operator and the notion of a generalized quasideterminant.
  We also introduce the notion of a dispersionless Adler type series, which is
applied to the study of dispersionless Hamiltonian equations. Non-commutative
Hamiltonian equations are discussed in this framework as well.
