Recent content by bruno321

Hi. I'm trying to prove this "little fact": let M, N be finitely generated modules over a PID. Then if M+M=N+N (where = means isomorphism and + means direct sum) then M=N. I'm sure it can be done with the structure theorem (it is obvious from the hypotheses); it looks like it should be...

Well, I managed to do it differently. I didn't realize the exercise preceding this one was going to help me :P This other exercise said that if S is a connected surface, f: S->R a differentiable function, and the differential of f is always 0, then f is a constant function. This is easily...

Homework Statement Show that if all normals to a connected surface pass through the origin, the surface is contained in a sphere. Homework Equations The Attempt at a Solution I know a surface is locally the graph of a differentiable function, so in a neighbourhood of a point p, the...