Theorems · Theorem · field theory
IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {α : E},
IsAlgebraic F α → Field.finSepDegree F ↥F⟮α⟯ = (minpoly F α).natSepDegreeThe separable degree of F⟮α⟯ / F is equal to the separable degree of the
minimal polynomial of α over F.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Fintype.cardproof · cited by 1,386
- IntermediateFieldstatement · cited by 988
- Nat.cardproof · cited by 844
- minpolystatement and proof · cited by 439
- IntermediateField.adjoinstatement and proof · cited by 382
- Multiset.toFinsetproof · cited by 230
- Nat.card_eq_fintype_cardproof · cited by 200
- IsAlgebraicstatement and proof · cited by 163
- Nat.card_congrproof · cited by 133
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iffproof · cited by 4