1 and so worked out the case for C. (It is a PID) K: OK now do C^n. F&S helped me in proving that the ideals can be the functions that vanish not only at the point but also on a complex line, eg. K: OK now do the ring of functions locally C^infty(R) around 0. After quite a bit of hinting I said the ideal of functions with a 0 of infinite order at 0 is not principal. I eventually managed to prove it too. F asked me to leave the room and after a few seconds all 3 came out and shook my hand, congratulating me. (for what I have no idea). Comments: All three created a pleasant atmosphere, to the extent that my tenseness allowed it. They want to see you come up with ideas of your own. Especially for the algebra questions, it is hard to describe the enthusiasm that overcame Schlag and Fefferman when I mentioned anything that could be conducive to a solution.