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. Suppose (Z, +, ·) is an integral domain. Furthermore, assume that there exists subsets N...

. Suppose (Z, +, ·) is an integral domain. Furthermore, assume that there exists subsets N and N0 of Z such that both (Z, N, +, ·) and (Z, N0 , +, ·) satisfy all of the axioms of the integers. Prove that N = N0 .

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