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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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  • $\begingroup$ is this a homework problem? $\endgroup$ Jul 6, 2010 at 13:46
  • $\begingroup$ Nope, I would have said if it was. :) $\endgroup$
    – yatir
    Jul 6, 2010 at 13:49
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    $\begingroup$ Hopefully, you are not required to satisfy both (i) and (ii) with the same $A$ and $B$. $\endgroup$
    – PersonX
    Jul 6, 2010 at 13:53

1 Answer 1

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

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  • $\begingroup$ When you're right, you're right. thanks. $\endgroup$
    – yatir
    Jul 6, 2010 at 13:49

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