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    Ring Isomorphism

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    Let gcd(m, n) = 1. We know that Zmn = Zm × Zn as an additive group. Is
    there a ring isomorphism Zmn = Zm × Zn? Same question for the complex
    numbers C with C = R × R as an additive group.

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    Solution Summary

    The presence of ring isomorphisms is ascertained. The solution is detailed and well presented.