I have a battery light on in 91 honda accord been through 3 alternators in a week.?

I have a 91 accord, alternator died, for sure cause it shut off and died on the way home, about a week ago. I went to autozone got a new one put it in, it worked for the week fine no light and to my suprise a week later, my battery light is on so today i went to autozone and according to their tester this alternator is bad, so i pulled it in the parking lot and put in ANOTHER new one. battery light was still on brought the tester back out and it says again, its bad. Now being a backyard and current student for mechanics, i kno in old systems if you disconnect the positive from battery and it keeps running, alternators good. i did the same test on my car, it runs. Any input? I have no idea......I'm lost.