I am reading Nicholson: Introduction to Abstract Algebra Section 6.2 Algebraic Extensions.

On page 282 the Corollary to Theorem 5 states the following: (see attachment for Theorem 5 and the Corollary)

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Corollary.Let be fields and let be algebraic over F .

If , then v is also algebraic over F and divides .

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The proof begins as follows:

"Proof.Here ... ... etc etc

My problem is as follows:

How do you show formally and explicitly that

Would appreciate some help.

Peter