  We consider gauged U(1) extensions of the standard model of particle physics
with three right-handed sterile neutrinos and a singlet scalar. The neutrinos
obtain mass via the type I seesaw mechanism. We compute the one loop
corrections to the elements of the tree level mass matrix of the light
neutrinos and show explicitly the cancellation of the gauge dependent terms. We
present a general formula for the gauge independent, finite one-loop
corrections for arbitrary number new U(1) groups, new complex scalars and
sterile neutrinos. We estimate the size of the corrections relative to the tree
level mass matrix in a particular extension, the super-weak model.
