The Stacks project

Definition 29.47.3. Let $X$ be a scheme.

1. We say $X$ is seminormal if every $x \in X$ has an affine open neighbourhood $\mathop{\mathrm{Spec}}(R) = U \subset X$ such that the ring $R$ is seminormal.

2. We say $X$ is absolutely weakly normal if every $x \in X$ has an affine open neighbourhood $\mathop{\mathrm{Spec}}(R) = U \subset X$ such that the ring $R$ is absolutely weakly normal.