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 $R'$.

## Comments (2)

Comment #1504 by Kollar on

Comment #1508 by Johan on