Theorems · Theorem · field theory
Field.finInsepDegree_eq_of_equiv
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type w) [inst_3 : Field K] [inst_4 : Algebra F K] (i : E ≃ₐ[F] K), Field.finInsepDegree F E = Field.finInsepDegree F K
If E and K are isomorphic as F-algebras, then they have the same finite
inseparable degree over F.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement and proof · cited by 1,681
- Cardinal.toNatproof · cited by 153
- Cardinal.toNat_liftproof · cited by 41
- Field.insepDegreeproof · cited by 23
- Field.finInsepDegreestatement · cited by 15
- Field.lift_insepDegree_eq_of_equivproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.finInsepDegree_botproof · cited by 0