Lemma 31.4.4. Let $X$ be a locally Noetherian scheme of dimension $\leq 1$. The following are equivalent

$X$ is Cohen-Macaulay, and

$X$ has no embedded points.

Lemma 31.4.4. Let $X$ be a locally Noetherian scheme of dimension $\leq 1$. The following are equivalent

$X$ is Cohen-Macaulay, and

$X$ has no embedded points.

**Proof.**
Follows from Lemma 31.4.3 and the definitions.
$\square$

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