Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 101 / 4 / c / ii

Table of contents
- Solution ii

Solution

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.

Solved by gpt-5.6-sol high.

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