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Add information to definition S_k
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aisejohan committed Sep 1, 2019
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Expand Up @@ -41620,9 +41620,11 @@ \section{Serre's criterion for normality}
\end{definition}

\noindent
Any Noetherian ring has property $(S_0)$ (and so does any finite module
over it). Our convention that $\dim(\emptyset) = -\infty$ guarantees
that the zero module has property $(S_k)$ for all $k$.
Any Noetherian ring has property $(S_0)$ and so does any finite module
over it. Our convention that the depth of the zero module is $\infty$
(see Section \ref{section-depth}) and the dimension of the empty set is
$-\infty$ (see Topology, Section \ref{topology-section-krull-dimension})
guarantees that the zero module has property $(S_k)$ for all $k$.

\begin{lemma}
\label{lemma-criterion-no-embedded-primes}
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