Explore BrainMass

Explore BrainMass

    Module proof

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com October 9, 2019, 7:44 pm ad1c9bdddf

    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 ...

    Solution Summary

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