Let E be an extension field of F Let E be algebraic of odd degree over F Show that 2 is algebraic of odd degree over F, and F() F( 2 ) ...

Because F is a finite extension of F and 2 F Theorem 313 shows that 2 is alg ...

Let E be an extension field of F. Let E be algebraic of odd degree

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Let E be an extension 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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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 09, 2023 01:43 AM

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Let E be an extension field of F. Let E be algebraic of odd degree

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Because F is a finite extension of F and 2 F Theorem 313 shows that 2 is alg...View the full answer

A First Course In Abstract Algebra

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