Prime chain
= Prime chain
{title2=$P_0\subsetneq\cdots\subsetneq P_s$}
A strictly increasing finite sequence of <prime ideals>. Its length is the number of strict inclusions, so the displayed chain has length $s$. The <Krull dimension> of a ring is the supremum of such lengths; the <height of a prime ideal> restricts to chains ending at that prime.