# 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"?

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

= m, but for S = R {0}, S

^{−1}R is a ﬁeld, with rad S^{−1}R = 0.Need a fast expert's response?

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