  We investigate supersymmetric models where neither R-parity nor lepton number
nor baryon number is imposed. The full high energy theory has an exact
horizontal U(1) symmetry that is spontaneously broken. Quarks and Higgs fields
carry integer horizontal charges but leptons carry half integer charges.
Consequently, the effective low energy theory has two special features: a U(1)
symmetry that is explicitly broken by a small parameter, leading to selection
rules, and an exact residual Z_2 symmetry, that is lepton parity. As concerns
neutrino parameters, the Z_2 symmetry forbids contributions from R_p-violating
couplings and the U(1) symmetry induces the required hierarchy. As concerns
baryon number violation, the Z_2 symmetry forbids proton decay and the U(1)
symmetry provides sufficient suppression of double nucleon decay and of neutron
- antineutron oscillations.
