\begin{definition}[Definition:Height (Ring Theory)]
Let $A$ be a commutative ring.
Let $\mathfrak p$ be a prime ideal in $A$.
The '''height''' of $\mathfrak p$ is the supremum over all $n$ such that there exists a chain of prime ideals:
:$\mathfrak p_0 \subsetneqq \mathfrak p_1 \subsetneqq \cdots \subsetneqq \mathfrak p$
{{explain|make this precise, as in Definition:Krull Dimension of Ring}}
Category:Definitions/Ring Theory
\end{definition}