Please see the attached file for the fully formatted problem.
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.
The presence of ring isomorphisms is ascertained. The solution is detailed and well presented.