Re: [math-fun] Possibly naive question about algebraic numbers

The theorem Gareth proves seems very basic, so I wonder if it has a name and attribution.

I wondered the same when I needed (a slight variant of) it for my PhD thesis, but I didn't find it elsewhere after a short search. I ended up saying "I'm sure this must be well known to those who know such things" and giving substantially the same proof as I did upthread. :-) I agree that it seems very basic, and it surely must be very well known. Perhaps it's regarded as too obvious to bother mentioning. There's probably a one-line proof using Groebner bases. -- g