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)
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) 


$\mathbb{Q} \subset \mathbb{Q}[x_0, \dots, x_n] \subset \mathbb{Q}(x_0, \dots, x_n)$. 

