In a ring , a nonzero element is said to be a zero divisor if there exists a nonzero such that .
For example, in the ring of integers taken modulo 6, 2 is a zero divisor because . However, 5 is not a zero divisor mod 6 because the only solution to the equation is .
1 is not a zero divisor in any ring.
A ring with no zero divisors is called an integral domain.
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