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What is the example of a Noetherian local ring of dimension one which is not a discrete valuation ring.

rschwieb
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Babai
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2 Answers2

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Take the local ring of any curve singularity, for instance localize $k[x,y]/(x^2-y^3)$ at $(x,y)$.

MooS
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Take the ring of polynomials over a noetherian local ring with Krull dimension 0, say $\mathbf Z/p^2\mathbf Z$, localised at the maximal ideal $\langle (p\mathbf Z/p^2\mathbf Z, X\rangle$. Or the ring of formal power series over the same ring.

Babai
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Bernard
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