Lemma 10.119.3. Let $R$ be a local ring with maximal ideal $\mathfrak m$. Assume $R$ is Noetherian, has dimension $1$, and that $\dim (\mathfrak m/\mathfrak m^2) > 1$. Then there exists a ring map $R \to R'$ such that
$R \to R'$ is finite,
$R \to R'$ is not an isomorphism,
the kernel and cokernel of $R \to R'$ are annihilated by a power of $\mathfrak m$, and
$\mathfrak m$ is not an associated prime of $R'$.