  In the Supersymmetric extension of the Standard Model with minimal particle
content the three neutrinos can have non trivial masses and mixings, generated
at 1 loop due to renormalizable lepton number violating interactions. We show
that the resulting mass matrix can provide simultaneously a significant amount
of the Dark Matter of the Universe and solve the solar neutrino problem, if the
free parameters of the model are fixed to values which are consistent with all
the present accelerator and cosmological constraints. The theory also predicts
new effects in future experiments looking for neutrino oscillations.
