# Punctured spectrum of a (reduced) Noetherian local ring of dimension $1$ is an affine- scheme?

Let $$(R, \mathfrak m)$$ be a Noetherian local ring of dimension $$1$$. Then the affine- scheme $$X=\operatorname {Spec}(R)$$ can be written as a set-theoretic union $$\operatorname{Spec}(R)=Min(R)\cup \{\mathfrak m\}$$.

So if $$U=\operatorname{Spec}(R)\setminus \{\mathfrak m\}$$ is the punctured spectrum, then $$U$$ is a finite set and every point is a closed point (under the subspace topology), even more, every Singleton set is an irreducible component. In particular, $$\dim U=0$$.

My question is: Is $$(U, \mathcal O_X|_U)$$ an affine- scheme ? If it is indeed an affine-scheme, then it is the Spectrum of an Artinian ring (as $$U$$ is a Noetherian scheme of dimension zero), in which case, can we identify the global section ring $$\Gamma_U(U)$$ ?

I'm willing to assume $$R$$ is reduced if that helps.

Note that $$U$$ is a discrete topological space, so the structural sheaf over $$U$$ is simply a product of the rings of stalks at each point. In particular, if $$V \subset U$$ is open, clearly $$\mathcal{O}_U(V)=\prod_{x \in V}{\mathcal{O}_{U,x}}=\prod_{p \in V}{R_p}$$.
But each such $$R_p$$ is a ring with a single prime ideal: so that $$(U,\mathcal{O}_U)$$ is the spectrum of the product of the $$R_p$$ over $$p \in Min(A)$$.