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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.

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