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  "body": "\n## Summary\n\nThe support of a [[module|0NZ8JA25WK]] $M$ over a [[commutative ring|0310REJJY8]] $R$ is the set of [[prime ideals|00MHHZ9SNE]] $\\mathfrak p$ at which the [[localization|68E0F8N94E]] $M_{\\mathfrak p}$ is nonzero.\nIt is a subset of the [[spectrum|FB45BHHA2J]] of $R$, and it tells where on that space the module \"lives\".\nFor a [[finitely generated module|05QY1VEBYD]], it is the closed set of primes containing the [[annihilator|HB4XDKJTW8]] of $M$.\n\n## Explanations\n\n### L1 human\n\nThink of the prime ideals of $R$ as points and of the module as something spread over these points.\nThe support is the set of points where the module is not zero.\nFor the integers, the module $\\Z/6\\Z$ lives only at the primes $2$ and $3$, since every other prime becomes invertible and kills it.\nThe [[definition|B0223N93XS]] makes this precise.\n",
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