Suppose m, n ∈ Z + are relatively prime. The function f : Zmn → Zm × Zn defined by  f([Z]mn) = ([Z]m, [Z]n) is well-defined, and is a bijection.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 25E
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Suppose m, n ∈ Z + are relatively prime. The function f : Zmn → Zm × Zn defined by  f([Z]mn) = ([Z]m, [Z]n) is well-defined, and is a bijection.

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