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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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When a finitely generated ideal is contained in a union of maximal ideals

For a commutative ring $R$ with 1, it is well known that if an ideal is contained in the union of all maximal ideals, then it contained in one of them. I want to know why the following is true or is …
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