Most likely the problem is your alternator....the battery light actually does not monitor battery condition, only the charging system.
I'd check the voltage regulator and the fuses first. The fuses are the cheapest fix and the voltage regulator will run about 25% less than an alternator.
Your battery could need replaced, your alternator or starter could be going bad. It is best to have a mechanic look at it if this bothers you or it continues.
Inside the alternator
It could be an alternator. Check with a mechanic if that is the issue.
battery hooked up backward, wires crossed somewhere or it could be the solenoid.
you have a short where negative is touching the metal of the car or it is grounded inproperly
Well, It could be your battery or alternator or both needs to be replaced but it could just be loose or corroded battery cables
chances are it's the voltage regulatorit could also be a wire no connected on the alternator
could be the alternator or starter sounds like the alternator if the battery is gone flat get the alternator tested at auto parts or garage jump charging the battery might get you out of trouble for a bit
it could mean that you have a loose battery cable that needs to be tightened
The ground cable, on the battery may need to be tightened or cleaned. The alternator voltage regulator may need to be replaced.
It could be the starter in it. It may be weak or need replaced.
If your battery is not fully functioning and needs to be replaced, it can make the alternator work harder. This could cause a brand new alternator to go bad. Check your battery, if the battery is not the issue, return the alternator, it should have a warranty on it for at least the first 30 days.