Theorems · Theorem · field theory
Irreducible.natSepDegree_dvd_natDegree
∀ {F : Type u} [inst : Field F] {f : Polynomial F}, Irreducible f → f.natSepDegree ∣ f.natDegreeThe separable degree of an irreducible polynomial divides its degree.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement and proof · cited by 1,105
- Irreduciblestatement and proof · cited by 496
- ExpCharproof · cited by 276
- Polynomial.natSepDegreestatement · cited by 53
- ExpChar.existsproof · cited by 11
- Polynomial.HasSeparableContractionproof · cited by 8
- Irreducible.hasSeparableContractionproof · cited by 4
- Polynomial.HasSeparableContraction.dvd_degreeproof · cited by 1
- Polynomial.HasSeparableContraction.natSepDegree_eqproof · cited by 1
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