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Exercise 2.106.2 Let F be a field, and let a be a nonzero element of F. Let b be an arbitrary element of F. Prove that the map f: Fa]→ Fr] that -> sends x to ax +b and more generally, a polynomial po+P1x++ Pn to the polynomial po + P1(ax +b) + .+ pn(ax + b)" is an automorphism of F[a].

Exercise 2.106.2 Let F be a field, and let a be a nonzero element of F. Let b be an arbitrary element of F. Prove that the map f: Fa]→ Fr] that -> sends x to ax +b and more generally, a polynomial po+P1x++ Pn to the polynomial po + P1(ax +b) + .+ pn(ax + b)" is an automorphism of F[a].

Advanced Engineering Mathematics
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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Exercise 2.106.2 Let F be a field, and let a be a nonzero element of F. Let b be an arbitrary element of F. Prove that the map f : Fa→ Fx that sends x to ax +b and more generally, a polynomial po+P1x+ + Pnt" to the polynomial po + pı(ax + b) + + Pn(ax + b)" is an automorphism of Fa].
Transcribed Image Text:Exercise 2.106.2 Let F be a field, and let a be a nonzero element of F. Let b be an arbitrary element of F. Prove that the map f : Fa→ Fx that sends x to ax +b and more generally, a polynomial po+P1x+ + Pnt" to the polynomial po + pı(ax + b) + + Pn(ax + b)" is an automorphism of Fa].
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