.The Ring Z of integers (mod n) is an integral domain if and only if
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Definition 1.4. A ring R is an integral domain if R = {0}, or equivalently 1 = 0, and such that r is a zero divisor in R ⇐⇒ r = 0. Equivalently, a nonzero ring R is an integral domain ⇐⇒ for all r, s ∈ R with r = 0, s = 0, the product rs = 0 ⇐⇒ for all r, s ∈ R, if rs = 0, then either r = 0 or s = 0.
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