Answered: Let E be an extension of field of F.…

Let E be an extension of field of F. Let α ∈ E be algebraic of odd degree over F. Show that α2 is algebraic of odd degree over F, and F(α) = F(α2).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 5E: Let F be a field and f(x)=a0+a1x+...+anxnF[x]. Prove that x1 is a factor of f(x) if and only if...

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Let E be an extension of field of F. Let α ∈ E be algebraic of odd degree over F. Show that α² is algebraic of odd degree over F, and F(α) = F(α²).

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