2001 Mazda Alternator Bad???
 

The battery light came on 3 days ago and stays on. The battery reads 12.54 volts after sitting all night and the reads 14.39-14.4 volts when the car is running at idle and at 2200 rpm, which would indicate that the alternator and battery are fine. I have also driven at night with the lights, radio and heater running for the past 3 nights and days. Any ideas?

2001 Mazda Protege 2.0 LX