  A Poisson analog of the Dixmier-Moeglin equivalence is established for any
affine Poisson algebra $R$ on which an algebraic torus $H$ acts rationally, by
Poisson automorphisms, such that $R$ has only finitely many prime Poisson
$H$-stable ideals. In this setting, an additional characterization of the
Poisson primitive ideals of $R$ is obtained -- they are precisely the prime
Poisson ideals maximal in their $H$-strata (where two prime Poisson ideals are
in the same $H$-stratum if the intersections of their $H$-orbits coincide).
Further, the Zariski topology on the space of Poisson primitive ideals of $R$
agrees with the quotient topology induced by the natural surjection from the
maximal ideal space of $R$ onto the Poisson primitive ideal space. These
theorems apply to many Poisson algebras arising from quantum groups.
  The full structure of a Poisson algebra is not necessary for the results of
this paper, which are developed in the setting of a commutative algebra
equipped with a set of derivations.
