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.
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