 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-101/4/c/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Yes. Scalar multiplication in the quotient module gives directly

R_{n} (M / N) = {r (m + N) : r \in R_{n}, m \in M} = (R_{n} M + N) / N = (M_{n} + N) / N .

Hence the displayed filtration is precisely the induced filtration.

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