Question

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)" ?

Answer 1

If we take R = Z and S=Z2Z. Here,rad S^−1R =2Z₍₂₎ and R ∩ rad S^−1R =2Z, but radR =0.So, this inclusion in not true ingeneral.