Question

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

i) dimA-dimB>n

ii) dimB-dimA>n

(where dim is the krull dimension)

Yatir

Answer 1

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