What is an example of a noetherian local integral domain $R$ of Krull dimension 1?

Question

As stated in the title I am interested in examples of noetherian local integral domains $R$ of Krull dimension 1.

Answer 1

You may consider for instance discrete valuation rings. Archetipal examples of such rings are

• the local ring $\mathcal{O}_{X, \, x}$ of a smooth curve $x$ at a point $x \in X$;
• the ring $\mathbb{Z}_p$ of $p$-adic integers (for any prime $p$);
• the ring $\mathbb{K}[[x]]$ of formal power series in one variable $x$ over some field $\mathbb{K}$.