PA-28 Flight Instructor with student received an alternator failure alert during takeoff roll. The takeoff was rejected; and the aircraft returned to the ramp.

Narrative

I was doing a take off and landing flight with my student. On the 6th lap of our flight on the takeoff roll at about 55 KIAS we received an alternator failure alert. I promptly took controls and aborted the takeoff. We exited the runway and followed ATC instructions to contact ground once clear of the runway. Upon clearing the runway I ran the alternator failure checklist and noticed that the alternator amps were still indicating normally and that the battery amps still read '0'. We contacted ATC and requested to taxi back to our FBO. Ground Control asked if we needed any assistance. Upon double checking that all systems were operating normally and assuring that we could taxi safely we told them that we did not need assistance. They advised me to stay on frequency as they checked with their supervisor to ensure they did not need any more information. They then advised me that they did not need any more information. We completed our taxi back to the ramp. The alternator failure annunciator and alarm remained on the entire time while the amps still indicated normally. We completed the shutdown procedure and exited the aircraft with no further incident.