Answered: on field of finite degree. Show that…

on field of finite degree. Show that every k-endomorphism of F is an automorphism of F. Give an example, with justification to show that this may f

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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Let F/k be an extension field of finite degree. Show that every k-endomorphism of F is an automorphism of F. Give an example, with justification to show that this may fail to hold for arbitrary extensions.

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