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Spin-dependent transport through the CdTe/CdMgTe/CdMnTe/CdMgTe/CdTe heterostructure is investigated theoretically. Using the transfer matrix method and the effective-mass approximation, the effect of resonant states on spin transport is studied in a magnetic semiconductor resonant tunneling diode. The magnetic field dependences of the transmission coefficients, current densities, and tunnel magnetoresistance for the considered system have been studied. The doping and temperature effects on the current are also investigated theoretically. The numerical results show that the CdMnTe layers, which act as spin filters, polarize the electric currents. This spin splitting of the energy levels enables one to select the resonant condition for the desired spin by adjusting the magnetic field or the applied bias. The spin-up component of the current-density shows a strong suppression for increasing magnetic fields; the total current density is dominated by the spin-down component. It is also found that the tunnel magnetoresistance depends strongly on the magnetic field and the applied voltage.