If p(x)∈F[x] and deg p(x) = n, show that the splitting field for p(x)over F has degree at most n!.
If p(x)∈F[x] and deg p(x) = n, show that the splitting field for p(x)over F has degree at most 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 14E
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If p(x)∈F[x] and deg p(x) = n, show that the splitting field for p(x)
over F has degree at most n!.
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