Definition:Krull Dimension of Ring

Definition
Let $(R,+,\circ)$ be a commutative ring with unity.

The Krull dimension of $R$, often denoted $\operatorname{K-dim} (R)$ 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$