+ ao be monic, separable, 2. Let f(x) = E[x], f(x) = x² + An-1xn-1 which splits over E. Let ☀ € Aut(E) fix the set of roots, ƒ(a) = 0 ⇒ f(o(a)) = 0. Prove that (ak) = ak for all k.
+ ao be monic, separable, 2. Let f(x) = E[x], f(x) = x² + An-1xn-1 which splits over E. Let ☀ € Aut(E) fix the set of roots, ƒ(a) = 0 ⇒ f(o(a)) = 0. Prove that (ak) = ak for all k.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![2. Let ƒ(x) = E[x], ƒ(x) = x² + An−1x²−¹ + + ao be monic, separable,
which splits over E. Let
e Aut(E) fix the set of roots, f(a) = 0 ⇒
f(o(a)) = 0. Prove that (ak) = ak for all k.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b3b5d99-82ff-4b2c-a339-8b5827a89088%2F6166abaf-2900-4129-8e8c-ddebe72754c2%2Faubepu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let ƒ(x) = E[x], ƒ(x) = x² + An−1x²−¹ + + ao be monic, separable,
which splits over E. Let
e Aut(E) fix the set of roots, f(a) = 0 ⇒
f(o(a)) = 0. Prove that (ak) = ak for all k.
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