2003 Liberty ?s

The computer controls the charging system on those.
There should be a code stored related to the charging system causing the light to come on.
You should have a two wire plug on the alternator, one is power from pcm/asd relay and the other is field/ground control from pcm.

I would do as suggested take the alternator off and have checked , If its ok then it could be a wiring issue or bad pcm.