Prove that a h:G→A(G) a given by h(c)=θc​ , is an injective hom... | Filo
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SOLVED:Show that every homomorphism π1(S^1) →π1(S^1) can be realized as the induced homomorphism φ* of a map φ: S^1 →S^1.
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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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