The conditions under which it is possible to reduce a Poisson manifold via
a regular foliation have been completely characterized by Marsden and Ratiu
. In this Letter we show that this characterization can be generalized in a
natural way to the singular case and, as a corollary, we obtain that when
the singular distribution is given by the tangent spaces to the orbits crea
ted by a Hamiltonian Lie group action, one reproduces the Universal Reducti
on Procedure of Arms, Cushman, and Gotay. Mathematics Subject Classificatio
ns (1991): 70H33, 58F05, 53C80.