# Structure theorem for non-Noetherian local rings

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 $S$?

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