## rings with ‘flat functions’

Let (R,m) be a local ring over a field. Suppose the ring has flat elements, i.e. m∞≠{0}. (The prototype is of course C∞(Rp,0), or a quotient of it, by some finitely generated ideal.) 1. For which rings and ideals, J⊂R, the following holds. If the completions satisfy ˆJ⊇(ˆm)N then J⊇mN+n, for some finite n. At … Read more