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Zero divisor

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In a ring R, a nonzero element a\in R is said to be a zero divisor if there exists a nonzero b \in R such that a\cdot b = 0.

For example, in the ring of integers taken modulo 6, 2 is a zero divisor because 2 \cdot 3 \equiv 0 \pmod 6. However, 5 is not a zero divisor mod 6 because the only solution to the equation 5x \equiv 0 \pmod 6 is x \equiv 0 \pmod 6.

1 is not a zero divisor in any ring.

A ring with no zero divisors is called an integral domain.


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