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Ring Theory : Prove that an R-module M is Noetherian if and only if every submodule of M is finitely generated.

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Prove that an R-module M is Noetherian if and only if every submodule of M is finitely generated.

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It is proven that an R-module M is Noetherian if and only if every submodule of M is finitely generated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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