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  "body": "\n## Definition\n\nA commutative ring is a [[ring|0894J980RK]] $R$ such that $a \\cdot b = b \\cdot a$ for all $a, b \\in R$.\n\n## Remarks\n\nThe integers $\\mathbb{Z}$, the rational numbers $\\mathbb{Q}$ and the polynomials in one variable over $\\mathbb{Q}$ are commutative rings.\nThe ring of $2 \\times 2$ real matrices is not commutative.\nEvery [[field|0QA8CHH8MG]] is a commutative ring.\n\n## Explanations\n\n### L1 human\n\nIn a commutative ring, the order of the factors in a product does not matter.\nThe integers are the model: $3 \\cdot 5 = 5 \\cdot 3$.\n",
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