Let K be a field extension of F and let a ?K. Show that [F(a):F(a3)] ? 3. Find examples to illustrate that [F(a):F(a3)] can be 1, 2, or 3.

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Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition

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Problem 13E

Let K be a field extension of F and let a ?K. Show that [F(a):F(a3)] ? 3. Find examples to illustrate that [F(a):F(a3)] can be 1, 2, or 3.

Step-by-Step Solution:
##### Textbook: Contemporary Abstract Algebra

##### Edition: 8th

##### Author: Joseph Gallian

##### ISBN: 9781133599708

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###### Chapter 21, Problem 13E is Solved

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Let K be a field extension of F and let a K. Show that

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