Definition 29.47.3. Let $X$ be a scheme.

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.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.

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