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Describe all ring homomorphisms of Z×Z into Z×Z. [Hint: Note that if ϕ is such a homomorphism, then ϕ((1,0))=ϕ((1,0))ϕ((1,0)) and ϕ((0,1))=ϕ((0,1))ϕ((0,1)). Consider also ϕ((1,0)(0,1)).]

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