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Let  be a nonzero element of a ring  .
The element  is a left zero divisor if there exists a nonzero element  such that
 . Similarly,  is a right zero divisor if there exists a nonzero element  such that
 .
The element  is said to be a zero divisor if it is both a left and right zero divisor. A nonzero element  is said to be a regular element if it is neither a left nor a right zero divisor.
Example: Let
 . Then the elements  and  are zero divisors, since
 .
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