sider the integers Z as a Z-module. Let n be a non-zero integer and define a function fn :ZZ by fn(a) = na (a) Prove that fn is a Z - module homomorphism. (b) Use fn to prove that Z and nZ are isomorphic as Z - modules (c) Let g: Z→ Z be any Z-module homomorphism. Prove that g = fn for some integer n (Hint: consider g(1))

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