A zero divisor in a ring is an element that, when multiplied by a nonzero element, results in zero. This can occur on either side of the multiplication operation. According to the definition, the element 0 is always a zero divisor [1] [3]. In the ring of integers taken modulo 6, for example, both 3 and 4 are zero divisors because 3*4 = 12 ≡ 0 [4] [8]. A ring with no zero divisors is called an integral domain [4]. The concept of zero divisors helps identify a phenomenon where some rings may have zero divisors, while others may not [5] [6]. In the context of matrices over a ring R, a matrix is a zero divisor if there exists a nonzero vector v over R such that the product is zero [7].