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Answer to Question #24899 in Abstract Algebra for jeremy

Question #24899
Let R be a k-algebra where k is a field. Let K/k be a separable algebraic field extension.
Show that Nil*(RK) = (Nil*(R))K.
Expert's answer
Since Nil*(R) ⊆Nil*(RK), we have (Nil*(R))K ⊆Nil*(RK). On the other hand,RK/(Nil*R)K ∼ (R/Nil*R)K
is semiprime, so (Nil*(R))K⊇ Nil*(RK). Therefore, the desired equality follows.

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