Definition 10.141.1. Let $\varphi : B' \to B$ be a ring map. We say $\varphi$ is a small extension if $B'$ and $B$ are local Artinian rings, $\varphi$ is surjective and $I = \mathop{\mathrm{Ker}}(\varphi )$ has length $1$ as a $B'$-module.

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