 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-3/10e/b/ii/solution

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

Take

R = Z

and

I = (2)

. The ideal

I

is maximal, but

Z [X] / I [X] ≅ F_{2} [X]

is not a field, since

X

is nonzero and not invertible. Therefore

I [X] need not be maximal .

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