  R-parity-violating supersymmetry with a conserved baryon number B provides a
framework for particle physics with lepton number (L) violating interactions.
Two important probes of the L-violating physics are neutrino masses and
sneutrino-antisneutrino mass-splittings. We evaluate these quantities in the
context of the most general CP-conserving, R-parity-violating B-conserving
extension of the minimal supersymmetric standard model. In generic
three-generation models, three sneutrino-antisneutrino mass splittings are
generated at tree-level. In contrast, only one neutrino mass is generated at
tree-level; the other two neutrinos acquire masses at one-loop. In many models,
the dominant contribution to the radiative neutrino masses is induced by the
non-zero sneutrino-antisneutrino mass splitting.
