Like Jeremey said. Stick a volt meter on the battery with the key off. Check voltage. Should be right around 12.5v.
Turn the ignition on and start the car. Check the voltage. Should be about 13.7v.
If it's significantly over that, then that's why the battery light is on. If it's under that, then that's why the battery light is on.
If it's just fine, then a diode in the alternator failed that's in the circuit that drives the idiot light. It's rare for such a part to fail without the regulator circut also having a failure, but I suppose it's possible.