Height of a prime ideal
= Height of a prime ideal
{title2=$\operatorname{ht}P=\dim R_P$}
The height of a <prime ideal> is the supremum of lengths of strict <prime chains> ending at it, equivalently the <Krull dimension> of its <localization at a prime ideal>. The <Krull height theorem> bounds the height of a minimal prime over an $n$-generated <ideal> by $n$.