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Answer to Question #22735 in Abstract Algebra for Irvin

Question #22735
Let R be a commutative domain and S^(−1)R be the localization of R at a multiplicative set S.
Is "R ∩ rad S−1R ⊆ rad R" ?
Expert's answer
This inclusion in not true ingeneral.If we take R = Z and S=Z2Z.
Here, rad S−1R =2Z(2)and R ∩ rad S−1R =2Z, but rad R =0.

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