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Answer to Question #22734 in Abstract Algebra for Irvin

Question #22734
Let R be a commutative domain and S^(−1)R be the localization of R at a multiplicative set S.
Is "rad R ⊆ R ∩ rad S−1R"?
Expert's answer
This inclusion in not true ingeneral. Let’s take a commutative local domain (R,m) with nonzero m. Then rad R
= m, but for S = R {0}, S−1R is a field, with rad S−1R = 0.

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