Theorems · Theorem · field theory
Field.finSepDegree_mul_finSepDegree_of_isAlgebraic
∀ (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] [inst_5 : Algebra E K] [IsScalarTower F E K] [Algebra.IsAlgebraic E K], Field.finSepDegree F E * Field.finSepDegree E K = Field.finSepDegree F K
If K / E / F is a field extension tower, such that K / E is algebraic, then their
separable degrees satisfy the tower law
$[E:F]_s [K:E]_s = [K:F]_s$. See also Module.finrank_mul_finrank.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- Nat.cardproof · cited by 844
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Nat.card_congrproof · cited by 133
- Field.finSepDegreestatement · cited by 24
- Nat.card_prodproof · cited by 24
- Field.Embproof · cited by 12
- Field.embProdEmbOfIsAlgebraicproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- Field.finSepDegree_eqproof · cited by 2
- Field.finSepDegree_eq_finrank_iffproof · cited by 2
- Field.finSepDegree_dvd_finrankproof · cited by 1
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1