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By requiring the lower limit for the lightest right-handed neutrino mass,obtained in the baryogenesis from leptogenesis scenario, and a Dirac neutrinomass 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 theneutrinoless double beta decay, $m_{\nu_e}$ around $5\cdot10^{-3}$ eV and$m_{ee}$ smaller than $ 10^{-3}$ eV, respectively. The allowed range for themass of the heaviest right-handed neutrino is centered around the value of thescale of B - L breaking in the SO(10) gauge theory with Pati-Salam intermediatesymmetry.Comment: 9 pages, RevTex4. Revised, title change

BOUNDS FOR NEUTRINOLESS DOUBLE BETA DECAY IN SO(10) INSPIRED SEESAW MODELS