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.
Solution Preview
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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