Let char K = p 0 and let K[x] be irreducible of degree n.
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Let char K = p ≠ 0 and let ∫ ϵ K[x] be irreducible of degree n. Let m be the largest nonnegative integer such that ∫ is a polynomial in xPm but is not a polynomial in xpm+1. Then n = nopm. If u is a root of ∫, then [K(u) : K]s = no and [K(u) : K]i = pm.
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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