Let F/K be a field extension and a, b E F be algebraic over K. If...

 

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Let F/K be a field extension and a, b E F be algebraic over K. If a has degree m over K and b 0 has degree n over K, prove that the elements a+b, ab, ab, ab-1 have degree at most mn over K. Let F/K be a field extension and a, b E F be algebraic over K. If a has degree m over K and b 0 has degree n over K, prove that the elements a+b, ab, ab, ab-1 have degree at most mn over K.

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To prove that the elements a b ab a b and ab 1 have degree at most mn over K we need to show that their minimal polynomials have degree at most mn Let ... View the full answer