Definition:Krull Dimension

Definition

Let $\left({R, +, \circ}\right)$ be a commutative ring with unity.

The Krull dimension of $R$, often denoted $\operatorname{K-dim} \left({R}\right)$ is the maximal length of a chain of prime ideals:

$\mathfrak p_0 \subsetneqq \mathfrak p_1 \subsetneqq \cdots \subsetneqq \mathfrak p_{n-1} \subsetneqq \mathfrak p_n \subseteq R$

Source of Name

This entry was named for Wolfgang Krull.