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(a) Prove Fitting's Lemma : If M is an artinian module and f : M ⟶M is an injective homomorphism, then f is surjective. (b) Prove the dual assertion to Fitting's Lemma: If M is a noetherian module and f: M ⟶M is a surjective homomorphism, then f is injective. (c) Let G be a free abelian group of finite rank, and let ϕ: G ⟶G be an epimorphism. Show that ϕis an isomorphism. | Numerade
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