Lemma 10.126.11. Let $R$ be a ring. Let $I \subset R$ be an ideal. Let $S \to S'$ be an $R$-algebra map. Assume that

$I$ is locally nilpotent,

$S/IS \to S'/IS'$ is an isomorphism,

$S$ is of finite type over $R$,

$S'$ of finite presentation over $R$, and

$S'$ is flat over $R$.

Then $S \to S'$ is an isomorphism.

## Comments (1)

Comment #213 by Rex on