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The Jacobson–Bourbaki theorem is a result in the field of algebra, specifically in the theory of rings and algebras. It provides a characterization of the Jacobson radical of a ring in terms of the ideal structure of that ring. The theorem can be stated as follows: Let \( R \) be a commutative ring with unity, and let \( \mathfrak{m} \) be a maximal ideal of \( R \).

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