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  "body": "\n## Summary\n\nA multiplicative set in a [[commutative ring|0310REJJY8]] is a subset that contains $1$ and is closed under multiplication.\nThese sets are exactly the sets of elements that one may turn into units by [[localization|4C1AE84N5N]].\nThe complement of a [[prime ideal|00MHHZ9SNE]] and the set of powers of one element are the two main examples.\n\n## Explanations\n\n### L1 human\n\nThink of a multiplicative set as a list of allowed denominators.\nIf you may divide by $s$ and by $t$, then you may also divide by $st$, so the list must be closed under products.\nYou may always divide by $1$, so $1$ is on the list.\nIn the integers, the powers $1, 2, 4, 8, \\ldots$ form a multiplicative set, and allowing them as denominators gives the fractions $a / 2^k$.\nThe [[definition|PCH3G8BJ9Y]] gives the precise conditions.\n",
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