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  "body": "\n## Definition\n\nLet $R$ be a [[ring|0894J980RK]].\nAn element $a \\in R$ is a left zero divisor if there is a nonzero $x \\in R$ with $a x = 0$.\nAn element $a \\in R$ is a right zero divisor if there is a nonzero $y \\in R$ with $y a = 0$.\nAn element is a zero divisor if it is a left or a right zero divisor.\n\n## Remarks\n\nIn a [[commutative ring|0GYGHKX834]], left and right zero divisors are the same.\nIn $\\mathbb{Z}/6\\mathbb{Z}$, the classes of $2$ and $3$ are zero divisors, because $2 \\cdot 3 = 0$.\nSome authors do not count $0$ as a zero divisor. With the definition above, $0$ is a zero divisor of every nonzero ring.\nA [[unit|019NFGFPR5]] is never a zero divisor.\n\n## Explanations\n\n### L1 human\n\nIn the integers, a product is zero only when one factor is zero.\nIn other rings this can fail.\nIn the integers modulo $6$, $2 \\cdot 3 = 6 = 0$, but neither $2$ nor $3$ is zero.\n",
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