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Question: Is there an easy way to check that an integral domain is not an EUD?

I know that we have the implication that if $R$ is an EUD it is a PID, so if we can show $R$ is not a PID then it is not an EUD. This seems like the simplest way to check if something is not an EUD, find an ideal which isn't generated by a single element. But because all we need for an integral domain to be an EUD is a norm function, is there in general no easy way to show that no such norm function exists?

Irving Rabin
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    No, there is no easy way in general, see this duplicate and its answers: "To my knowledge, given an arbitrary integral domain, there is no "general" method to figure out whether it is a Euclidean domain or not." – Dietrich Burde Jan 10 '23 at 12:30

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