# Non-Noetherian ring

I am wondering if there are applications of non-noetherian rings (domains). Are there areas where it is applicable ? Now obviously there is an academic interest in it. But I want to know if there are areas where one might find an application, such as in algebraic statistics etc.

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You put "domains" in parentheses... does that mean you only want domains or ...? –  rschwieb Mar 5 '14 at 23:17

Often function rings are not noetherian and these sorts of rings come up frequently in applications, though what one counts as an application in mathematics obviously depends on who you are talking to. For instance, the ring of continuous functions from $\mathbb{R}$ to $\mathbb{R}$ is not noetherian.