 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/20g/c/i/solution

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

Given a nonzero fractional

I

, scale it to an integral ideal

a I

. By (i),

(a I) J = (r)

for some nonzero ideal

J

. Then

I^{- 1} = a r^{- 1} J

is fractional and

I I^{- 1} = R

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