# Answer to Question #22736 in Abstract Algebra for Irvin

Question #22736

Let R be a commutative domain and S^(−1)R be the localization of R at a multiplicative set S.

Is "rad S−1R ⊆ S−1(rad R)" ?

Is "rad S−1R ⊆ S−1(rad R)" ?

Expert's answer

If we take R = Z and S=Z2Z. Here,rad S

^{−1}R =2Z_{(2)}and R ∩ rad S^{−1}R =2Z, but radR =0.So, this inclusion in not true ingeneral.
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