Show that Let K be an extension of a field F and a e K be algebraic over F. Then F[a] = F (a), where F[a] = f(a) : f (x) e F [x]}. %3D
Show that Let K be an extension of a field F and a e K be algebraic over F. Then F[a] = F (a), where F[a] = f(a) : f (x) e F [x]}. %3D
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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