Proof that lf K[x] is monic irreducible, deg 2, and has all its
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Proof that lf ∫ ϵ K[x] is monic irreducible, deg ∫≥ 2, and ∫ has all its roots equal (in a splitting field), then char K = p ≠ 0 and ∫ = xPn - a for some n ≥ 1 and a ϵ K.
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2 2 To prove this statement we will use the following facts and theorems The fact that a polynomial is monic irreducible over a field K if and only if ...View the full answer
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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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