  The possibility of generating neutrino mass through see-saw mechanism
involving U(1) chiral Peccei-Quinn and scale symmetries breakdown is discussed.
We consider a generic scale invariant model which has three Majorana fermions
and a complex scalar singlet, which might be the one responsible for an
invisible axion, and we perform a summation of all leading logarithmic
radiative corrections to the tree level potential. The effective potential so
obtained is stable and drives the scalar field to a nonzero vacuum expectation
value according to the Coleman-Weinberg mechanism. As a result, right-handed
neutrinos gain mass at the Peccei-Quinn scale which is suggestive for
explaining very light active neutrinos. We illustrate the whole idea with the
addition of the Standard Model, and also a SU(3)$_L\otimesU(1)_X$ model in
which the subgroup SU(2)$_L\otimesU(1)_Y$ is constrained to be broken as an
effect of the effective potential. This last model presents electric charge
quantization as well.
