I know that for prime ideals $\text{ht}(P)+\dim(A/P)\leq \dim A$. I know that the result holds for any ideal $I$. Any hint on how to show this? I tried taking a minimal prime of $I$, and trying to estimate, but didn't get too far, since I don't know much on the structure of $\mathrm{Spec}(A)$. Thanks!
2026-03-29 10:26:45.1774780005
Dimension formula
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