Do prestigious mathematics journals discriminate against young (undergraduate) authors?
In fact, I published a paper in the Journal of Algebra based on work I did as an undergraduate (I was a graduate student by the time it was published).  

Certainly, there's no policy discriminating against undergrads (or anyone for that manner).  It's hard to rule out very subtle ways that cues affect people's judgement; it's actually quite rare that I am asked to referee a paper by someone I've never heard of, so I do notice and probably adopt a more skeptical attitude when asked to referee a paper by someone whose work I have no experience with. Still, this is a subtle effect, and there's nothing to be done about but to do good work and get your name out there.  

Actually, there's a decent chance that the editors and referee won't notice that you are an undergrad.  (If they do notice, it will likely because you are affiliated with a university where they expect to know any professor in your field, and thus will investigate when they see an unfamiliar name.)