  An anomaly-free U(1) gauge extension of the standard model (SM) is presented.
Only one Higgs doublet with a nonzero vacuum expectation is required as in the
SM. New fermions and scalars as well as all SM particles transform nontrivially
under this U(1), resulting in a model of three active neutrinos and one sterile
neutrino, all acquiring radiative masses. Charged-lepton masses are also
radiative as well as the mixing between active and sterile neutrinos. At the
same time, a residual $Z_2$ symmetry of the U(1) gauge symmetry remains exact,
allowing for the existence of dark matter.
