  We perform a many-body study of the spin dephasing due to the
D'yakonov-Perel' effect in n-typed GaAs (100) quantum wells under high magnetic
fields in the Voigt configuration by constructing and numerically solving the
kinetic Bloch equations. We include all the spin conserving scattering such as
electron-phonon, the electron-nonmagnetic impurity as well as the
electron-electron Coulomb scattering in our theory and investigate how the spin
dephasing time (SDT) is affected by the initial spin polarization, impurity,
and magnetic field.
  The dephasing obtained from our theory contains not only that due to the
effective spin-flipping scattering first proposed by D'yakonov and Perel' [Zh.
Eksp. Teor. Fiz. {\bf 60}, 1954 (1971)[Sov. Phys.-JETP {\bf 38}, 1053 (1971)]],
but also the recently proposed many-body dephasing due to the inhomogeneous
broadening provided by the DP term [Wu, J. Supercond.:Incorp. Novel Mechanism
{\bf 14}, 245 (2001); Wu and Ning, Eur. Phys. J. B {\bf 18}, 373 (2000)]. We
are able to investigate the spin dephasing with extra large spin polarization
(up to 100 %) which has not been discussed both theoretically and
experimentally. A huge anomalous resonance of the SDT for large spin
polarizations is predicted under the high magnetic field we used.
