Just wondering if anyone can help me diagnose this problem

1. Alternator is starting to make a audible whining type noise
2. Seems to increase in pitch and volume when engine revs
3. Battery symbol on dash display comes up to indicate that battery is not charging
4. When I unplug the battery cable from the alternator both the noise and battery symbol disappears
5. Checked the serpentine belt and all looks ok. No slippage, no belt problems.

So my tentative conclusion is that the alternator is gone (car has done around 130,000kms). Can anyone confirm this based on the symptoms I've described?

And also what are my options? Replace or try to fix? I hear that sometimes the bearing in the alternator goes or maybe some other part within the alternator.