Let K be the splitting field of f(x)=F(x) and let p(x) be an irreducible factor off(x) in F(x). If the roots of p(x) are a\index{1},a\index{2},...o\index{i}, then for each ithere exists an automorphism σ\index{i} in G(K,F) such that \index{i}(a\index{1})=0\index{i}.

Given : Let K be the splitting field of f(x)∈F(x) and let p(x) be an irreducible factor of f(x) in…

Answered: Let K be the splitting field of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 3E: 3. Let be an integral domain with positive characteristic. Prove that all nonzero elements of...

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Let K be the splitting field of f(x)=F(x) and let p(x) be an irreducible factor of f(x) in F(x). If the roots of p(x) are a\index{1},a\index{2},...\index{i}, then for each i there exists an automorphism o\index{i} in G(K,F) such that \index{i} (a\index{1})=\index{i}.