Start your engine and disconect the battery, if the car shuts off the alternator doesn't work or has blown a fuse.
if the engine runs without the battery connected the alternator is fine.
Could be the voltage regulator but I never experienced that kind of problem on my car... yet

so i dunno how to help ya there.
I had bad starts when my MAF Sensor was dirty. sometimes it would turn off, but for the rest of the day the car would run fine.
Actually now that think about it, it looked like the voltage regulator and I CEL.
The car would just lose power and I would give it some gas and finally get it going. and if I let it die it would just die.
Turned out to be a dirty MAF. So might want to look into that to if that is the problem.
Are you getting bad MPG or response?
or hard to climb from like 70-80 or 90 mph
But if the voltage light came on it could be the regulator just dunno how that works.