Zero Divisor

Zero Divisor

In abstract algebra, two nonzero elements a and b of a ring are respectively called a left zero divisor and a right zero divisor if a b = 0; this is a partial case of divisibility in rings. An element that is either a left or a right zero divisor is simply called a zero divisor. An element w that is both a left and a right zero divisor, is called a two-sided zero divisor. If the ring is commutative, then the left and right zero divisors are the same. A non-zero element of a ring that is not a zero divisor is called regular.