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Module proof

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If N and P are submodules of M that is an R-module and modules (N intersects P) and (N+P) are finitely generated then show that modules N and P are finitely generated.

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Solution Summary

This is a proof regarding modules and exact sequences. The second isomorphism theorem is examined.

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Consider the exact sequence

0 --> N n P --> N --> N/(N n P) --> 0

now, by the second isomorphism theorem

(N + P)/P ~ N/(N n P)

(where 'n' denotes intersection)

since ...

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