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Let a be a nonzero algebraic element over F of degree n. Show thata-1 is also algebraic over F of degree n.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 22E: Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].

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Let a be a nonzero algebraic element over F of degree n. Show that
a^-1 is also algebraic over F of degree n.

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