 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-101/4/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

p

r

p_{0} ⊊ p_{1} ⊊ \dots ⊊ p_{r} = p .

I

, without assuming

I

prime, is

ht (I) = p \supseteq I in f ht (p) .

R

dim R = sup {r : p_{0} ⊊ \dots ⊊ p_{r} are prime ideals of R} .

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