Explore BrainMass
Share

Explore BrainMass

    R-module proof

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

    Any help would be greatly appreciated. Please see the attached file. Thank you!

    Let R be a ring with identity. Recall that the non-zero R-module M is simple...

    © BrainMass Inc. brainmass.com October 9, 2019, 9:05 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/module-proof-rings-172953

    Attachments

    Solution Preview

    Please see the attachment.

    Suppose that is a commutative ring and that is an ideal of . Show that the -module is simple if and only if is a maximal ideal..
    Proof:
    " ": Suppose that is simple. I want to show that is a maximal ideal. If not, then we can find ...

    Solution Summary

    This is a proof that the R-module is simple if and only if I is a maximal ideal.

    $2.19