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 $S$?

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    $\begingroup$ 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


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


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