If E is an extension of F and f(x) belong to F[x] and if phi is an automorphism of E leaving every element of F fixed prove that pgi must take a root of f(x) in E into a root of f(x) in E
If E is an extension of F and f(x) belong to F[x] and if phi is an automorphism of E leaving every element of F fixed prove that pgi must take a root of f(x) in E into a root of f(x) in E
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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pgi is phi
![If E is an extension of F and f(x) belong to F[x] and if phi is
an automorphism of E leaving every element of F fixed
prove that pgi must take a root of f(x) in E into a root of
f(x) in E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaea6d9f-c5a6-423e-bb0f-24f62709ecc2%2Fad7f4876-f216-4ece-b329-0cd712006e35%2Fz5r40od_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If E is an extension of F and f(x) belong to F[x] and if phi is
an automorphism of E leaving every element of F fixed
prove that pgi must take a root of f(x) in E into a root of
f(x) in E
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