  Commutative rings in which every prime ideal is the intersection of maximal
ideals are called Hilbert (or Jacobson) rings. We propose to define classical
Hilbert modules by the property that {\it classical prime} submodules are the
intersection of maximal submodules. It is shown that all co-semisimple modules
as well as all Artinian modules are classical Hilbert modules. Also, every
module over a zero-dimensional ring is classical Hilbert. Results illustrating
connections amongst the notions of classical Hilbert module and Hilbert ring
are also provided. Rings $R$ over which all $R$-modules are classical Hilbert
are characterized. Furthermore, we determine the Noetherian rings $R$ for which
all finitely generated $R$-modules are classical Hilbert.
