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R-module proof

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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...

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Solution Summary

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

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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..
" ": Suppose that is simple. I want to show that is a maximal ideal. If not, then we can find ...

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