Use Exercises 30 and 36 to show that every finite field is of prime-power order, that is,

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Use Exercises 30 and 36 to show that every finite field is of prime-power order, that is, it has a prime-power number of elements.

Data from Exercise 30

Let E be an extension field of a finite field F, where F has q elements. Let α ∈ E be algebraic over F of degree n. Prove that F(α) has qⁿ elements.

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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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Use Exercises 30 and 36 to show that every finite field is of prime-power order, that is,

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Let E be a finite field with prime subfield Z p If E Z p then ...View the full answer

A First Course In Abstract Algebra

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