All Questions

Let $R$ be a regular local complete (with respect to the maximal ideal) ring with field of fraction $K$. Let $S\cong R[[x_1,\cdots, x_n]]/J$ (this is a Noetherian local ring which is an $R$-algebra) ...

I am studying the following article https://www.math.nagoya-u.ac.jp/~takahashi/tc9.pdf The main theorem is the Theorem 3.3. Howewer, I have the following questions about the proof: How does it help ...

A question asked by a friend. I believe it's false, but lack a decisive counterexample. This question shows that it is true for valuation rings, but I know too little about them. In the wider ...