Theorem 11.5: The group ℤm ×ℤn is cyclic (hence isomorphic to ℤmn) if and only if gcd(m, n) = 1.
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Prove that the rings ℤmn and ℤm ⊕ℤn are isomorphic if and only if m and n are relatively prime.Hint: Consider a ring homomorphism ℤmn→ℤm ⊕ℤn.
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