Theorems · Theorem · field theory
IsSepClosed.degree_eq_one_of_irreducible
∀ (k : Type u) [inst : Field k] [IsSepClosed k] {p : Polynomial k}, Irreducible p → p.Separable → p.degree = 1- Defined in
- Mathlib.FieldTheory.IsSepClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- Irreduciblestatement and proof · cited by 496
- Polynomial.Separablestatement and proof · cited by 117
- IsSepClosedstatement and proof · cited by 41
- Polynomial.Splits.degree_eq_one_of_irreducibleproof · cited by 5
- IsSepClosed.splits_of_separableproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsSepClosed.algebraMap_surjectiveproof · cited by 2