We have studied the low-temperature photoluminescence of the two-dimensional electron gas in a single GaAs quantum well in magnetic fields up to 50 T over four orders of magnitude of illumination intensity. At the very highest illumination powers, where the recombination is excitonic at zero field, we find that the binding energy of both the singlet and triplet states of the negatively charged exciton (X-) increase monotonically with the applied field above 15 T. This contradicts recent calculations for X-, but is in agreement with adapted calculations for the binding energy of negative-donor centers. At low-laser powers we observe a strong transfer of luminescence intensity from the singlet (ground) state to the tripler (excited) state as the temperature is reduced below 1 K. This is attributed to the spin polarization of the two-dimensional electron gas by the applied magnetic field. [S0163-1829(99)01104-2].