2
$\begingroup$

Is there a structure theorem (like Cohen 's structure theorem) for non-Noetherian local rings?

I am adding what I am looking for as someone asked in the comment.

If $R$ is a local domain (not necessarily complete) containing a field $k$ , then I am looking for something like that there exist $S=k[[x_1,x_2, \ldots, ..]]$ (infinitely many variables if $R$ has infinite Krull dimension ) such that $ S \subset R$ and $R$ is finitely generated as a module over $S$?

$\endgroup$
2
  • 1
    $\begingroup$ Can you elaborate a bit more? What are you looking for? You can edit your question. $\endgroup$ Mar 16, 2016 at 9:59
  • $\begingroup$ I have edited the post @AndrásBátkai thanks. $\endgroup$
    – mukhujje
    Mar 16, 2016 at 18:47

1 Answer 1

1
$\begingroup$

Here is a paper by Nagata that provides an answer for rings satisfying Krull's intersection theorem.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.