Zero divisor

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.

See also

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