Theorems · Theorem · field theory
Polynomial.Separable.map_irreducible_of_isPurelyInseparable
∀ {F : Type u} (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {f : Polynomial F},
f.Separable → Irreducible f → ∀ [IsPurelyInseparable F E], Irreducible (Polynomial.map (algebraMap F E) f)If E / F is a purely inseparable field extension, f is a separable irreducible polynomial
over F, then it is also irreducible over E.
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- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
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