Theorems · Theorem · field theory
Polynomial.exists_separable_of_irreducible
∀ {F : Type u} [inst : Field F] (p : ℕ) [HF : CharP F p] {f : Polynomial F},
Irreducible f → p ≠ 0 → ∃ n g, g.Separable ∧ (Polynomial.expand F (p ^ n)) g = f- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- Nat.Primeproof · cited by 2,059
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- pow_zeroproof · cited by 1,094
- Polynomial.coeffproof · cited by 1,045
- Irreduciblestatement and proof · cited by 496
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.hasSeparableContractionproof · cited by 4