High Quality Content by WIKIPEDIA articles! In abstract algebra, a nonzero element a of a ring is a left zero divisor if there exists a nonzero b such that ab = 0. Similarly, a nonzero element a of a ring is a right zero divisor if there exists a nonzero c such that ca = 0. An element that is both a left and a right zero divisor is simply called a zero divisor. If multiplication in the ring is commutative, then the left and right zero divisors are the same. A nonzero element of a ring that is neither a left nor right zero divisor is called regular.

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