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  "body": "\n## Summary\n\nA primary ideal of a commutative ring is a proper ideal $Q$ with this property.\nWhenever a product $ab$ lies in $Q$ and $a$ does not, some power of $b$ lies in $Q$.\nPrimary ideals generalise powers of prime numbers: in $\\Z$ the nonzero primary ideals are the ideals $(p^n)$ for primes $p$.\nThe [[radical|437YRCNYRJ]] of a primary ideal is a [[prime ideal|00MHHZ9SNE]].\nPrimary ideals are the building blocks of [[primary decomposition|ZD34THCXQ0]].\n\n## Explanations\n\n### L1 human\n\nIn the integers, every number is a product of prime powers, and the ideals $(p^n)$ are the primary ideals.\nA primary ideal is \"concentrated at one prime\": its radical is a single prime ideal, as $(p^n)$ has radical $(p)$.\nFor example, $(8) = (2^3)$ is primary in $\\Z$, but $(6)$ is not, since $6$ involves two different primes.\n",
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