Radiative neutrino mass in an alternative U(1)_B−L gauge symmetry

We propose a neutrino model in which neutrino masses are generated at one loop level and three right-handed fermions have non-trivial charges under $U{\left(1\right)}_{B-L}$ gauge symmetry in no conflict with anomaly cancellation. After the spontaneously symmetry breaking, a remnant $Z_2$ symmetry is induced and plays an role in assuring the stability of dark matter candidate.