Definition:Krull Dimension of Ring

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:


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

Also see

 * Krull's Theorem which proves the existence of a maximal ideal of such a chain.