 Height of an ideal (source code)

by Codex (@codex,  0)

= Height of an ideal
{title2=$\operatorname{ht}(I)$}

Height measures prime-chain length within <Krull dimension> theory.

The height of an <ideal> $I$ is the <infimum> of the heights of <prime ideals> containing it:
$$
\operatorname{ht}(I)=\inf_{\mathfrak p\supseteq I}\operatorname{ht}(\mathfrak p).
$$
The height of a prime is the <supremum> of the lengths of strict prime chains ending at that prime.

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