  By requiring the lower limit for the lightest right-handed neutrino mass,
obtained in the baryogenesis from leptogenesis scenario, and a Dirac neutrino
mass matrix similar to the up-quark mass matrix we predict small values for the
$\nu_e$ mass and for the matrix element $m_{ee}$ responsible of the
neutrinoless double beta decay, $m_{\nu_e}$ around $5\cdot10^{-3}$ eV and
$m_{ee}$ smaller than $ 10^{-3}$ eV, respectively. The allowed range for the
mass of the heaviest right-handed neutrino is centered around the value of the
scale of B - L breaking in the SO(10) gauge theory with Pati-Salam intermediate
symmetry.
