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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)

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is this a homework problem? – Martin Brandenburg Jul 6 '10 at 13:46
Nope, I would have said if it was. :) – yatir Jul 6 '10 at 13:49
Hopefully, you are not required to satisfy both (i) and (ii) with the same $A$ and $B$. – Chris Phan Jul 6 '10 at 13:53
up vote 15 down vote accepted

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

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When you're right, you're right. thanks. – yatir Jul 6 '10 at 13:49

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