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