For all $n$, I need to find examples of rings $A\subset B$ such that:


i) $\dim A-\dim B\gt n$


ii) $\dim B-\dim A\gt n$


(where $\dim$ is the *Krull dimension*)



Krull Dimension
$\mathbb{Q} \subset \mathbb{Q}[x\_0, \dots, x\_n] \subset \mathbb{Q}(x\_0, \dots, x\_n)$.


