Noetherian ring that isn't euclidean? Can anyone give me an example of one? I know it's equivalent to finding a noetherian that isn't PID, but I'm not sure!
The ring of integers of $\mathbb{Q}(\sqrt{-19})$ is a principal ideal domain that is not Euclidean.
The ring of integers of $\mathbb{Q}(\sqrt{-19})$ is a principal ideal domain that is not Euclidean.