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  "body": "\n## Example\n\nThe zero ring is the set $\\{0\\}$ with the operations $0 + 0 = 0$ and $0 \\cdot 0 = 0$.\nIt is a [[commutative ring|0GYGHKX834]] in which $1 = 0$.\n\n## Remarks\n\nA [[ring|0894J980RK]] $R$ is the zero ring if and only if $1 = 0$ in $R$. If $1 = 0$, then $a = a \\cdot 1 = a \\cdot 0 = 0$ for each $a \\in R$.\nThe zero ring is not an [[integral domain|09S3PFBEPM]] and not a [[field|0QA8CHH8MG]], because these definitions require $1 \\neq 0$.\n\n## Explanations\n\n### L1 human\n\nThe zero ring has only one element.\nAll the axioms of a ring hold, but in a trivial way.\nIt is the only ring in which $1$ and $0$ are the same element.\n",
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