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In a [[ring]] <math>R</math>, a nonzero element <math>a\in R</math> is said to be a '''zero divisor''' if there exists a nonzero <math>b \in R</math> such that <math>a\cdot b = 0</math>.

For example, in the ring of [[integer]]s taken [[modular arithmetic | modulo]] 6, 2 is a zero divisor because <math>2 \cdot 3 \equiv 0 \pmod 6</math>.  However, 5 is ''not'' a zero divisor mod 6 because the only solution to the equation <math>5x \equiv 0 \pmod 6</math> is <math>x \equiv 0 \pmod 6</math>.

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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[[Category:Ring theory]]