The light indicates that the battery is providing the charge, and not the alternator. The alternator as been taken offline, whether for high or low voltage isn't really a concern; it's simply been taken offline.
The 152 does have separate procedures for a high charge rate vs. a failed alternator, however. In this case, the discharge light is one and the ammeter is showing a discharge, one may consider it a failed alternator and proceed with the low voltage light checklist.
The regulator isn't in the alternator; it's a separate box attached to the firewall. Failure of the regulator isn't uncommon, but then the same may be said of the alternator. An alternator belt may also have failed. I've had the pully come right off in flight before. Checking it should be part of every preflight.
The procedure for the low voltage light in the airplane will be spelled out in the emergency checklist, and should also be found in emergency procedures in the Pilot Operating Handbook. It's not really much of an emergency,but more of an abnormal situation.
The procedure requires turning off the avionics, checking that the alternator circuit breaker is in, then turning off both sides of the master switch. Turn the master switch back on (one side is the battery master, the other is the alternator), and check the ammeter to see that it's either neutral or that it's taking a load. If the low voltage light is out and the ammeter shows that the electrical system is restored, then turn on the avionics and continue. Otherwise, turn the alternator off, reduce electrical load and land as soon as practicable.