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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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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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