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  "body": "\n## Summary\n\nA prime ideal of a commutative ring is a proper ideal with the following property. If it contains a product, then it contains one of the factors.\nThe prime ideals of $\\mathbb{Z}$ are the ideals $p\\mathbb{Z}$ for $p$ prime and the zero ideal.\nThe [[definition of a prime ideal|06HC6HK0Z8]] gives the conditions.\n",
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