Alternator Light on all the time

I just had my alternator rebuilt, and it seems to be working fine, but the light in the dash is lit constantly (although dimly lit) Do i really have a charging problem, or is there an easy way to make the light stop coming on, aside from removing the bulb...I seem to recall another car i had years ago with the same problem and if you disconnected the battery and reconnected it, the light went out... tried that and it didnt work... unplugged the wires from the back, still didnt work... wondering if maybe the 'rebuild' wasnt so good...the light WASN'T on beforehand by the way, but the bearings were making noise. Any ideas?